This study investigates the mixing characteristics of non-Newtonian liquids flowing through a microfluidic channel equipped with a two-part cylinder, which possesses spatially varying zeta potentials and is subjected to a time-periodic electric field. A finite-element-based numerical framework is employed to solve the transport equations, governing the underlying mixing dynamics, using physically justified boundary conditions. The influence of amplification factor of the electric field amplitude, the angular velocity of the time-periodic forcing, the Carreau number, and the flow behaviour index, on the flow field, shear stress distribution, and mixing performance is systematically investigated. Results show that, at maximum potential of the applied field, the core flow velocity, magnitude of reverse flow velocity, and shear stress increase with increasing amplification factor, while these quantities decline at minimum potential. Consequently, temporal mixing efficiency exhibits a non-monotonic response due to competing effects of convective enhancement and attenuation. Despite this, both the maximum and average mixing efficiencies improve substantially at higher amplification factors relative to steady electric field operation. Increasing the angular velocity of the time-periodic field similarly enhances the effectiveness of mixing. It is shown that the flow behaviour index exerts minimal influence at low Carreau numbers due to negligible changes in apparent viscosity. In contrast, at higher Carreau numbers, reduced viscosity intensifies vortex formation, thereby increasing mixing efficiency, particularly for lower flow behaviour indices. The inclusion of Poincaré section, energy consumption ratio, and mixing performance improves the current analysis. Overall, the findings demonstrate that time-periodic electric fields can significantly augment mixing of non-Newtonian liquids, and seem to provide insights into the design of efficient micromixers, typically used for diagnostic applications.

Nanofluidic blue energy harvesting, based on salinity gradients, is strongly governed by ion selectivity and electrochemical coupling at the nanoscale. In this study, a comprehensive numerical framework is developed to investigate electrical energy generation, driven by coupled salinity and temperature gradients in a pH-sensitive polyelectrolyte layer (PEL) grafted nanochannel. The model incorporates temperature-dependent PEL ionization constants, ion partitioning effect arising from permittivity contrast, coupled electrothermal–ionic transport, and Soret-type thermo-diffusion effects. The modeling framework consisting of Poisson–Nernst–Planck (PNP) and energy equations has been solved using a finite-element approach and validated against established theoretical and experimental results. The numerical model is also validated against steady-state PNP solutions based on the classical nanochannel model. Results reveal that temperature-dependent PEL ionization critically regulates the space charge density and local pH distribution within the nanochannel. It is seen that increasing the right reservoir temperature (Tright) reduces the effective ionization strength of PEL functional groups. Besides, increasing local temperature shifts the neutral pH, at which the space charge density is zero, toward more acidic local conditions. It is shown that the ion partitioning effect induces a basic PEL region and an acidic core due to proton migration driven by Born energy differences. These coupled effects enhance cationic transport while suppressing anionic current at higher right reservoir pH (pHR), resulting in strong cation selectivity with transference numbers exceeding 0.5. The diffusion potential follows the trend in the transference number and is strongly dependent on pHR while it is mildly influenced by Tright. The enhanced ionic current consequently leads to a significant increase in the maximum pore power and power density with increasing pHR and Tright. Notably, the power density exceeds 5 W m–2 and the energy conversion efficiency, relative to the Gibbs free energy of mixing, surpasses 30% at alkaline pHR, highlighting the potential of PEL-modified nanochannels for efficient blue energy harvesting.

We experimentally investigate the effect of fluid rheology on wicking dynamics in paper-based LFA (lateral flow assay) using a NaCMC (sodium carboxymethyl cellulose)–water solution and human blood. We develop a saturation-based numerical framework to simulate the wicking phenomenon in paper-based porous strip using experimentally estimated effective viscosity of the solution. Increasing the NaCMC concentration leads to higher liquid entry pressure and enhances flow heterogeneity. Raman analysis unveil that the higher NaCMC concentrations result in more stable hydrogen bonding, primarily attributed to the enhanced hydroxyl group intensity, which in turn capable of increasing the effective viscosity by an order of magnitude. Consequently, we find that with increasing the concentration of NaCMC solution, the average wicking length and imbibition velocity decrease. Interestingly, the effective viscosity ratio appears to be less than unity at lower NaCMC concentrations at longer time instants. We show that diffusion and interception mechanisms dominate total trapping efficiency, while the contribution of inertial mechanism remains insignificant. With increase in NaCMC concentration, the diffusion and overall theoretical trapping efficiency follow a non-monotonic trend. The higher NaCMC concentrations in lower axial positions of the paper strip lead to an enhancement of both trapping efficiency and its probability. Pertaining to imbibition of human blood on paper strip, the wicking length and average wicking velocity of blood reduces with increase in hematocrit level and, at times, temporal variation of effective viscosity of blood shows a non-monotonic trend. Moreover, we find that, based on the critical Damk€ohler number, the optimum test line location is shorter for higher hematocrit level and increasing NaCMC concentration. This insight provides the optimum design guideline for LFA with efficient reaction. We believe that the findings of this endeavor are deemed pertinent to shed light on the role of fluid rheology in wicking phenomenon and analyte trapping for the efficient design of LFA, largely used for biochemical analysis of non-Newtonian biofluids.

We investigate the impact of plasma activated water (PAW) on the root development of Brassica juncea using a phytofluidic device. We prepared PAW with an adjusted pH level employing a state-of-the-art microbubble enhanced cold plasma activation (MB-CPA) technique. The results manifest that the root length and the number of cortical cells increases as the percentage of PAW rises up to 20%, attributed primarily to the enhancing nitrogen (N)-uptake trend. Whereas, beyond ∼20% PAW concentration, a limited root development (30 to 60% reduction) was observed due to the adverse effect of excess nitrate or nitrite ions of PAW, generating greater oxidative stress. Consequently, we obtain two distinct sets of Michaelis-Menten kinetics parameters for two N-uptake regimes in the window of PAW percentage under consideration. The higher magnitude of inward diffusive flux of N-uptake is evident at lower PAW percentages and lower at larger PAW percentages. Intriguingly, at a PAW percentage closer to 20%, the pectin's Raman peak intensity reaches its maximum value for cell signaling of nutrition transport. Similarly, the higher Young's modulus value for 20% PAW permits greater mechanical strength because of the enhanced lutein intensity. Besides, we performed numerical simulations of the flow field developed inside the device, and the simulated results also confirm that the mechanical stress at the root tip region is significantly reduced on the application of PAW. The inferences drawn from this analysis offer insights into how PAW influences plant-root development in sustainable agricultural techniques, including hydroponic systems.

Biochemical and medical diagnostics are two main fields in which vortex generation in microfluidic devices has several applications. Therefore, the aim of the present endeavor is to investigate the characteristics of a non-Newtonian vortex under the influence of a pH-sensitive polyelectrolyte layer (PEL)-modulated electroosmotic effect in a microchannel. Additionally, it is considered that the bulk solution pH (pHb0) and ionic concentration of the solution influence the zeta potential. Accordingly, the corresponding mathematical framework is constructed by using a numerical solver based on the finite element method and is subsequently verified against available experimental data in limiting conditions. Within the range of pHb0 and rheological parameters─Carreau number and flow behavior index─we critically analyze the PEL space charge density, net body force, and flow pattern. The current findings indicate that the existence of discrete net electrical body force patterns yields specific flow structures that enable substantial variation in the flow rate and mixing efficiency. The dominance of the basic PEL group protonic exchange at lower pHb0 and acidic PEL group protonic exchange at higher pHb0, respectively, permits positive and negative PEL space charge densities. Consequently, it is evident that the net electrical body force in PEL is extremely pHb0-dependent. Therefore, with smaller pHb0, the anticlockwise vortex with a negative flow rate is identified, whereas the clockwise vortex with a positive flow rate is predicted for larger pHb0. In turn, five distinct flow pattern regimes appear when the bulk solution pH pivots from 3 to 11. Remarkably, mixing efficiency exceeds 90% for greater diffusive Peclet numbers in highly acidic liquids. Overall, the outcomes of this study may significantly impact the design of microfluidic devices that mix and transport non-Newtonian liquids at particular pHb0 values.

The current study investigates how ambient temperature affects streaming potential-induced electrical energy generation triggered by nutrient flow in the stem xylem. During the experiment, the streaming potential of Brassica juncea is measured at various atmospheric temperatures, and the pressure gradient is computed for numerical simulations. It has been found that as atmospheric temperature rises, the increase in transpiration pull augments both axial and radial flow velocities. This enhances the flow loading at the intersection of the stem xylem core region and the porous pitted wall. Consequently, as atmospheric temperature increases, the mechanical stress inside the pitted porous wall also rises. Furthermore, due to convection-driven ionic transport, it becomes apparent that the magnitude of the induced potential at the bottom side of the stem xylem increases with rising atmospheric temperature. Additionally, owing to the ion-partitioning effect caused by differences in electrical permittivity, the concentration of K+ appears to be substantially lower in the pitted porous wall. As atmospheric temperature rises, the streaming electric field strengthens, enhancing both electrical and hydraulic power. Interestingly, atmospheric temperature has almost no influence on energy conversion efficiency. The insights drawn from this study contribute to a better understanding of the impact of atmospheric temperature on the development of green energy generation devices with high power densities.

This work investigates numerically the influence of electroosmotic vortex produced by positively charged patches on the reaction characteristics of two species A and B. By altering the patch zeta potential ratio and relative concentration of species B, the flow field, product concentration field, recirculation strength, product concentration flow rate, and production rate are evaluated. It is found that the generation of maxima concentration of species C (CC) is higher for the non-uniformly charged case, as well as, the prediction of maxima CC started more toward the upstream for the non-uniformly charged micro-reactor compared to the uniformly charged case. Additionally, patch zeta potential increases recirculation strength while decreasing product concentration flow rate. Up to a critical point, the production rate increases with a relative concentration increase of species B, after which it becomes insensitive. Moreover, the non-uniformly charged micro-reactor gives a higher production rate at a higher relative concentration of species B compared to the uniformly charged case. The results of the current study can be utilized to improve the design of micro-reactors used in the chemical and biological sectors.

This work estimates Michaelis-Menten kinetics parameters for nutrient transport under varying flow rates in the soft roots of Indian mustard (Brassica juncea) using a plant fluidic device. To find the metallic components within the roots, inductively coupled plasma mass spectrometry (ICP-MS) analysis was performed. The flow rate-dependent metabolic changes were examined using Raman spectral analysis. In addition, three-dimensional numerical simulations were conducted to assess mechanical stresses resulting from the concentration difference that enhances osmotic pressure and flow loading at the root-liquid interface. Convection, the primary mode of nutrient transport in flowing media, was observed to reduce nutrient uptake at higher flow rates. In contrast, diffusion became more prevalent in areas where the complex root structure restricted the flow field. The concentration gradient between the upstream and downstream regions of the root caused nutrient diffusion from downstream to upstream. As seen, an increase in flow rate resulted in a decrease in root length due to the reduction of advantageous metabolites, which led to lower average mechanical stress and osmotic pressure loading. Additionally, osmotic pressure at the root-liquid interface was found to increase over time. Numerical simulations revealed that the average internal mechanical stress was substantially greater when osmotic pressure was considered. This emphasizes the importance of accounting for osmotic pressure when assessing mechanical stress in roots. This study uses a fluidic device that replicates hydroponic conditions for the first time in order to evaluate the convection-dependent Michaelis-Menten kinetics of nutrient uptake in plant roots.

This study investigates cooling characteristics of electronic components integrated to a way-shaped canopy swayed by the forced convective air flow. Aluminum foam that is extremely conductive is used to cover the heat-generating component. The numerical framework developed in this endeavor takes into account the impact of conjugate transport of heat in the copper base and convective heat transport with ambient with plastic cover. Using the Darcy extended Brinkman–Forchheimer model to describe the flow field underneath the porous aluminum foam. By altering the pore size, simulations are performed to obtain the flow field, heat flux lines, maximum temperature rise, cooling performance, relative pressure drop, and thermal entropy formation. It has been seen that the distinct flow topology in the wavy channel, mainly stimulated by the additional vortices that form there compared to channel with plane wall, modifies the associated heat lines. Consequently, for a given flow condition, the usage of wavy wall permits approximately a 5 K drop in maximum temperature when compared to channel having plane wall. A larger pore size improves cooling performance because the wavy channel experiences a smaller relative pressure drop. Furthermore, the entropy generation owing to the thermal transport of heat is smaller in wavy channels and decreases gradually as pore size increases. Derived insights of this analysis are expected to have significant impact on designing cost-effective electronic cooling systems.

This study computationally investigates the effects of finite size of ion via steric factor and interfacial slip on heat transfer features of pure electroosmotic flow through a rectangular microchannel. Our results show that increasing ion size significantly affects the fluid flow rate with a pronounced reduction observed when interfacial slip is present. The heat transfer analysis reveals new insight into the variation of the Nusselt number under a constant wall heat flux condition. The average Nusselt number ( N u ¯ ) decreases with the steric factor at low Brinkman numbers while it increases at higher Brinkman numbers, indicating a critical Brinkman number that decreases with reduced electrical double layer thickness. Similarly, a critical Peclet number (Pe) is identified, below which N u ¯ decreases with Pe, and above which it increases. Notably, the combined effects of ion size and interfacial slip are particularly important at higher Pe and Debye parameters, leading to a substantial enhancement in heat transfer performance compared to cases with no-slip and point-sized ions. Furthermore, the heat transfer reduction due to the steric effect can be effectively mitigated by adjusting the slip length. This offers a promising strategy for optimizing micro-electro-mechanical thermo-fluidic systems and provides new insight into the impact of ion size and interfacial slip effects in microfluidic and electrokinetic heat transfer applications.

This study investigates the flow characteristics of a semi-diluted NaCMC-KCl aqueous solution in a charged nanochannel. A numerical model, consistent with ion transport mechanisms, is developed to analyze chemiosmotic flow under the influence of electrokinetic effects. The modeling framework employs a finite element-based approach to solve the governing equations and validate the theoretical predictions. We looked into how the bulk polyelectrolyte concentration, salt concentration in the left-side reservoir, and nanochannel height affect the mobile ions' space charge density, induced axial electric field, local viscosity, local and average flow velocity, and convective current. The findings show that the modulation of the degree of electrical-double layer (EDL) overlap with an increase in polyelectrolyte bulk concentration allows for an increase in mobile ion space charge density. The results of this analysis suggest that the concentrations of salt and polyelectrolyte have a significant impact on the local viscosity. The local viscosity increases with the increase in polyelectrolyte concentration and decreases with augmented left-side reservoir salt concentration. Furthermore, higher left-side reservoir salt concentrations result in an augmented convective current, while higher polyelectrolyte bulk concentrations lead to reduction of the same. Interestingly, modulation of the degree of EDL overlap with varied nanochannel heights yields non-intuitive flow patterns. In light of this, we established the critical bulk polyelectrolyte and left-side reservoir concentrations beyond which flow reversal occurs at greater nanochannel heights. The findings of this analysis are deemed pertinent to the development of state-of-the-art nanofluidic devices, largely used for chemiosmotic flow actuation of polyelectrolyte solutions.

Paper-based microfluidic devices are widely used in point-of-care diagnostics, yet the fundamental mechanisms governing analyte transport under partially saturated conditions remain insufficiently characterized. Here, we systematically investigate the concentration-dependent imbibition dynamics and particle trapping behavior of analyte/colloid-laden fluids in porous paper substrates. Using model food-dye colloids of varying particle sizes (∼0.3-4.5 μm) and concentrations (0.5-2 mg/ml), we quantify key saturation-dependent parameters and reveal their strong influence on wicking length and analyte retention. A semiempirical numerical model incorporating experimentally derived van Genuchten and Brooks-Corey parameters is developed to predict analyte flow under varying conditions. Our study demonstrates that particle size, concentration, and paper properties critically modulate transport behavior, with implications for reproducibility and sensitivity in lateral flow assays. Furthermore, through Damköhler number analysis, we propose practical design guidelines for optimal test line placement based on flow and reaction dynamics. This combined experimental and modeling framework offers new insights for the rational design and optimization of paper-based diagnostic platforms.

We investigate the heat transfer characteristics of electromagnetohydrodynamic electroosmotic flow in a rectangular microchannel by incorporating the steric effect along with the interfacial slip. The steric effect is represented by the bulk volume fraction of ions and is accounted through the steric factor ( υ ) . Our analysis systematically examines variations in the average Nusselt number ( N u ¯ ) by varying key parameters, including the Hartmann number ( H a ) , Debye parameter ( κ ) , lateral electric field parameter ( S ) , Joule heating parameter ( G ) , and dimensionless slip length ( β ) . The results reveal that the conventional point charge assumption leads to significant deviations in heat transfer predictions, overestimating N u ¯ for thicker electric double layers and underestimating it for thinner ones, with a critical Debye parameter ( κ =62.31) marking this transition. Notably, the deviation becomes more pronounced with increasing slip length and Hartmann number. Moreover, N u ¯ increases monotonically with H a for lower S and follows a non-monotonic decreasing-increasing trend for higher S . The presence of Joule heating not only enhances heat transfer at higher H a but also amplifies overprediction in N u ¯ due to the point-size assumption of ions. These findings provide crucial insights for optimizing micro-electro-magnetic-mechanical systems where precise thermal management and flow control are required.

We consider the influence of the ion-partitioning effect, enabled by the permittivity difference at the interface, to investigate the formation of blue energy within the nanochannel having pH-sensitive polyelectrolyte layer (PEL) under a salinity gradient. By altering the pH of right reservoir (pHR) and permittivity ratio of electrolyte solution to PEL, respectively, we investigated the electric-double layer (EDL) potential field, cationic concentration field, transference number, maximum power generation, optimum power production and its density, conductance, and optimum energy conversion efficiency. It turns out that due of the decrease in screening effect caused by the reduction in cationic concentration, the EDL potential is significantly increased by the ion-partitioning effect. We found that PEL permittivity and pHR have a considerable impact on ionic selectivity of nanochannel. For strongly acidic solutions, it implies that power generation decreases at smaller PEL permittivity. Additionally, at both lower and higher pHR values, the maximum energy conversion efficiency decreases as PEL permittivity decreases. Furthermore, the higher power generation density attained at lower pHR—an analysis conducted in this work, supports the novelty of the current energy-generating nanofluidic device when compared to the previously published work.

We examined the energy production assessment for heat flow of non-Newtonian ionic liquids within a wavy microchannel, considering the impact of finite ionic size and electroosmotic actuation induced by the applied electric field. A numerical method based on the finite element approach was utilized to determine the associated flow, electrical-double layer potential, and temperature fields. The current model was validated against existing theoretical results. Entropy production, including viscous, thermal, Joule, and total entropy generation within the wavy microchannel, was explored by varying the Brinkman number, thermal Peclet number, steric factor for finite ionic size, Carreau number, and dimensionless amplitude. Increasing the Carreau number resulted in higher shear-thinning behavior of the liquid, leading to higher total entropy generation. Conversely, an increase in finite ionic size reduced entropy generation. Entropy generation decreased with increasing amplitude of the wavy wall. Notably, compared to the plane channel, wavy microchannels consistently exhibited reduced entropy generation. The insights gained from this study are relevant to the development of efficient heat-exchanging devices for electronic cooling.

Motivated by the need for environmentally friendly energy-generating devices toward sustainable development and a secure energy future for the planet, the current work investigates high energy-density-producing devices utilizing the nanofluidic reverse electrodialysis approach, considering salinity gradients and pH influences in the ionic transport. Non-uniformly charged nanochannels have been considered to achieve the desired goal. This choice is expected to facilitate the regulation of the ionic field. The negative-positive-negative (NPN) and positive-negative-positive (PNP) surface-charged nanochannels are considered to be the non-uniform charged configurations. By altering the pH of the right-side reservoir (pHright) in comparison to the corresponding uniformly charged designs having positively charged walls and negatively charged walls, it was possible to compare the corresponding ionic and fluidic characteristics. By altering the pHright value, it becomes evident that the nanoslit’s unevenly charged surface can substantially affect the potential field and its gradient locally. The competition between cationic and anionic currents enables a highly cationic selective PNP nanoslit for the extremely acidic right reservoir. In contrast, the NPN nanoslit allows for greater anionic selectivity in the highly basic right reservoir. In addition, the PNP case achieves maximum electrical conductance, enabling a larger maximum generated power in the lower pHright range. Whereas, for the highly basic solution, electrical conductance as well as generated power were found to be higher for the NPN configuration. Remarkably, power density in the PNP and NPN configurations exceeds the commercial threshold limit in highly acidic and basic pHright values, respectively. We showed that the non-uniformly charged designs have higher average flow velocity or mass flow rate for almost every pHright (except close to pHright 4 and 10) under the salinity gradient. As such, information from this work can contribute to the development of more efficient nanofluidic devices that control flow and generate greater power density and flow rates.

We analyze the flow of KCl-water solution through negatively charged reservoir-connected nanochannels under the combined effects of varying salt concentration gradients and imposed temperature gradients. In our analysis, we account for the viscosity augmentation induced by the viscoelectric effect to enhance the prediction accuracy of the underlying transport characteristics. It has been found that the viscoelectric effect substantially increases wall viscosity, owing to the stronger transverse electric field. An increase in the zeta potential leads to a monotonic rise in wall viscosity, whereas increasing the nanochannel height results in an initial increase followed by a decrease. We show that the reduction in average flow velocity due to the viscoelectric effect is attenuated and recovered by the imposed temperature gradient within its physically permissible limits between reservoirs. Our findings reveal that the average flow velocity or mass flow rate is significantly influenced by changes in the potential induced in the electric double layer (EDL) due to variations in salt concentration between reservoirs. A greater degree of EDL overlap corresponds to higher average flow velocities, particularly when the left-side reservoir contains a higher concentration of salt due to a lower temperature therein compared with the right side. As the temperature differentials between reservoirs increase, the net current exhibits an increasing trend, while the average viscosity near the wall decreases. Moreover, within a specific range of salt concentrations in the left-side reservoirs, the temperature gradient is found to significantly enhance the average flow velocity. Notably, flow reversal is anticipated at higher salt concentrations in the left-side reservoirs. We believe that the findings of this endeavor have promising implications for the advancement of nanofluidic devices leveraging thermal energy in the permissible range to regulate mass transfer for biological applications.

We devised an economical method for droplet generation utilizing a “Y”-shaped paper strip. This approach employs passive capillary action, distinguishing it from traditional microfluidic droplet generators that require external pumping. To investigate the phenomenon of oil droplet generation in a water-wicking medium, we performed multiple experiments by changing the grade of paper (grades 1 and 4) and the inclination of the paper strip. Capillary pressure in the grade 1 paper surpasses that in the grade 4 paper at elevated liquid saturation levels. The microscopic droplets are produced within the pores and transported to the outlet by two primary mechanisms. These mechanisms entail the merging and elongation of oil droplets driven by the capillary action of water. The gravitational force markedly reduces the droplet size with considerable uniformity. We identified three regimes of temporal droplet generation based on the pattern of saturation-dependent capillary pressure. The type of paper used strongly influences the droplet size, with the smaller pore size of the grade 1 paper enabling the formation of smaller droplets. Finally, we established the temporal stability of the droplets, which is relevant for cellular research. To sum up, the results of this work provide a low-cost method for generating micro-sized droplets suitable for the chemical and biological investigation of micro- or nanoscale analytes.

We numerically investigate the mixing characteristics of non-Newtonian fluids under the ion-partitioning effect in a micromixer having a built-in patterned soft polyelectrolyte layer (PEL) on its inner wall surfaces. We show that the mixing phenomenon is greatly modulated by the migration of counter-ions triggered by the Born energy difference caused by the electrical permittivity differences between the PEL and bulk electrolyte. We demonstrate counter-ion concentration field, flow velocity variation, species concentration distribution, mixing efficiency and neutral species dispersion by varying the electrical permittivity ratio and rheological parameters. In contrast to the scenario of no ion-partitioning, results show that a decrease in counter-ions in the PEL permits a greater prediction of the induced potential field therein by the ion-partitioning effect. This phenomenon results in a higher electrical body force in the PEL at a lower permittivity ratio when the ion-partitioning effect is considered. Notably, for a lower permittivity ratio (= 0.2), the ion-partitioning effect results in an electrical body force that is significantly higher than that in the no ion-partition case. Consequently, when the ion-partitioning effect is present, we find that flow velocity and recirculation strength are an order of magnitude higher than those in the no ion-partitioning case. Furthermore, we revealed that because of the ion-partitioning effect, higher vortex strength at lower permittivity ratios leads to better species homogeneity and mixing efficiency. Thus, mixing efficiency surpasses 90% for lower permittivity ratio values. Neutral species dispersion is faster owing to the ion-partitioning effect, especially for higher Carreau numbers. Utilizing the ion-partitioning effect, the results of this study can be utilized to design and develop efficient micromixers intended for the mixing of non-Newtonian fluids for diagnostic applications.

We unveil the flow and ionic transport characteristics of xylem vessels to establish a correlation between in situ electrical energy generation and plant bioregulation. Scanning electron microscopy of the vascular bundles of Brassica juncea provides detailed features of lumen diameter and the porous pit structures of xylem walls. To investigate the nutrient transport and in situ electrical energy generation, we develop a two-dimensional modelling framework of the xylem vessel that is aligned with the experimental data. The solid wall model of the xylem vessel significantly underestimates axial flow resistance at higher inlet pressures, especially for smaller lumen diameters. Within the considered inlet pressure range, the under-prediction in axial flow resistance ranges from 3.14 % to 6.78 % and 0.37 % to 1.19 % for lumen sizes of 5 $mu$ m and 15 $mu$ m, respectively. Our analysis manifests that radial transport of ionic nutrients improves with increased porosity and permeability of the pitted porous wall. In the range of inlet pressure under consideration, it is shown that radial efficiency increases by 793.2 % to 471.9 % when the lumen diameter is reduced from 15 $mu$ m to 5 $mu$ m. The increased radial flow efficiency in narrower xylem vessels may support plant survivability under drought stress. Remarkably, we demonstrate that it is not the electrical potential alone, but the combined electrical and hydraulic power that influences plant growth. The amplified hydraulic and electrical power in plants with larger xylem vessels may promote growth attributed to more efficient ionic nutrient transport. We establish that the ratio of specific hydraulic conductivity to electrical conductivity acts as a potential indicator of plant health. This ratio increases with root-side inlet pressure; nevertheless, its dependence on lumen diameter is non-monotonic. The insights gained from the current work may advance the understanding of how in situ electrical stimulation regulates plant bioactivities.

Capillary osmotic (CO) transport of electrolytic liquids driven by a concentration gradient through charged nanopores is fundamentally important in many biological and industrial systems. Conventional models describing ionic transport in micro/nanofluidic systems often consider ions as point charges consistent with the mean-field theories. In nanofluidic geometries and at high electrolyte concentrations, finite ionic size, also known as the steric effect, significantly modulates the underlying transport, and classical theories fail to describe the transport phenomena accurately. To account for the steric effects on ionic transport in this endeavor, we modify the Nernst–Planck equation by incorporating an additional electrochemical potential using the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) model, which treats ions as hard spheres and is compared with the lattice-based Bikerman model. We consider three monovalent electrolytic (namely, LiCl, NaCl, and KCl) solutions with increasing cation hydrated radius, respectively, to investigate the steric effect modulated transport through the nanopore. Our analysis shows that finite ion size reduces counterion accumulation near the pore wall, with the BMCSL model predicting stronger exclusion compared to the Bikerman model. This reduced screening enhances the electrical double layer (EDL) potential magnitude and strengthens the induced axial electric field, which, in turn, augments the flow velocity relative to point-charge predictions. Our study also investigates the influence of a temperature gradient across the reservoirs in addition to the concentration gradient, thereby introducing thermodiffusion effects. The presence of thermodiffusion is found to diminish wall screening and enhance both the EDL potential and electric field strength, leading to a trigger in the net throughput. We believe that the insights gained from the present study on the temperature gradient-assisted transport of ionic liquids hold significant potential for advancing the design of next-generation temperature-sensitive biosensors and nanofluidic devices.

The present study intends to examine how the viscoplasticity of the liquid affects heat transfer characteristics in a wavy channel that contains metallic porous blocks, taking into account the effect of conductive heat flow within the finite wall thickness. Additionally, the second aim of this initiative is to establish an Artificial Neural Network (ANN) framework capable of forecasting the thermohydraulic performance factor and average Nusselt number based on different combinations of thermal and rheological parameters. To examine the flow field, conductive heat flux field, conductive heat lines, average Nusselt number, and performance factor, parameters such as the Darcy number, Bingham number, and thermal conductivity of the solid wall are varied within a justified range. It turns out that the flow field is significantly influenced by its fluid's viscoplastic characteristics, which allow the vortex to disappear at larger Bingham numbers. The average Nusselt number and performance factor show a monotonic increase with increasing Bingham numbers at higher Darcy numbers. The same exhibits a nonmonotonic tendency for lower Darcy numbers. Interestingly, the performance has been shown to have a value larger than unity, indicating that the current design has promising potential for use in applications involving thermal management of heat. The current ANN model predicts the average Nusselt number and performance factor with great precision. This endeavor represents the first exploration of how the viscoplastic properties of the liquid affect heat transfer characteristics within a wavy channel with metallic porous blocks, as well as the impact of conductive heat flow in solid walls.

Aquatic plants are key contributors to oxygen production and ecosystem stability. This study quantifies oxygen generation capacity of Hydrilla, Vallisneria, and Potamogeton under varying concentrations of potassium bicarbonate (KHCO3) using a dual-limb apparatus to measure oxygen output via water displacement. The experiment was complemented by gas chromatography-thermal conductivity detector (GC-TCD) analysis and numerical simulations to validate the results. An in silico diffusion model was developed to simulate oxygen release dynamics assuming uniform oxygen generation across plant surfaces and steady-state mass transport through the surrounding medium. The findings indicate that KHCO3 significantly enhances photosynthetic activity and oxygen production, with Hydrilla exhibiting the highest oxygen generation rate, followed by Potamogeton and Vallisneria. The optimal concentration of KHCO3 was determined to be 5 mg/mL, beyond which oxygen production declined due to osmotic stress and ionic imbalances. GC-TCD analysis confirmed oxygen (∼90%) as the primary gas produced, while simulated results closely aligned with the experimental data, reinforcing the robustness of the in silico analysis. This study highlights the role of bicarbonate ions in enhancing carbon availability for aquatic photosynthesis, thereby optimizing oxygen generation rate. The experimental methodology coupled with a numerical framework based on spatial diffusion model, as discussed in this endeavor, is novel in estimating oxygen generation rate from whole-plant in a closed system, enabling reproducible scaling for state-of-the-art environmental technologies. The insights gained from this in silico endeavor are expected to have broad implications for wastewater treatment (enhancing aerobic biodegradation), aquaculture (maintaining high dissolved oxygen), and carbon capture (biomass-based CO2 sequestration). Future research could focus on the exploration of long-term physiological effects of KHCO3 supplementation on oxygen generation and improvisation of modeling framework to incorporate biological feedback mechanisms into the underlying analysis.

We investigated the natural convective heat transfer characteristics within a solar power plant having a built-in aluminium metallic porous block and by using MWCNT-Fe3O4/water hybrid nanofluid. The Darcy-Brinkmann-Forchheimer model is used to describe the porous media flow field as well as the energy equation. When a metallic porous block is integrated to the plant, the average Nusselt number becomes significantly higher and increases with increasing Darcy numbers. The use of a hybrid nanofluid causes higher heat transfer rate compared to a pure fluid. Inferences obtained from this analysis are expected to provide a design basis of a modern solar plant intended for augmented energy recovery.

We investigated free convective heat transfer within an electronics cooling system with a metallic porous extension. The finite element method is used to solve the associated transport equations. Changing fluidic and geometric parameters allows examination of the isotherm contour, streamlines, and heater average temperature. It is found that the presence of a metallic porous block causes higher temperature up to a greater height of the domain than the absence of a porous material. The strength of the vortex is greater in the case of porous extension than in the case of no extension. Furthermore, the effect of Darcy number (Da) on average heater temperature (θavg) is negligible. The value of θavg decreases as the height of the porous extension increases. Inferences obtained from this analysis are expected to provide an adequate basis for the effective design of small-scale thermal management devices/systems that are typically used in electronic cooling systems.

The challenges of food security are exacerbated by the world's expanding population and diminishing agricultural land. In response, hydroponic cultivation offers a potentially more sustainable approach to growing nutrient-dense crops compared to traditional methods. Motivated by this understanding, we conducted a series of experiments to explore the behavior of Brassica juncea (Pusa Jaikisan) plant roots under various flow configurations within a controlled environment. The flow configurations considered were no-flow/flow (NF/F), continuous flow, flow/no-flow (F/NF), and stagnation. Additionally, we conducted anatomical sectioning of plant roots to study how different flow configurations affect the cellular structure of the plant root cross section. We also performed numerical simulations to investigate the internal stress generated within plant roots under various flow conditions. We observed that an increased number of cortical cells developed in response to higher internal stress in the case of continuous flow, which protected the inner vascular bundle from excessive biological stress. Comparing the designs, we found that continuous flow resulted in a longer root length compared to the F/NF and NF/F configurations. The root length per unit average flow power was highest for the 2 h F/NF case, followed by the 2 h NF/F, 3 h F/NF, and continuous flow cases. This suggests that periodic flow conditions (F/NF and NF/F) with lower average power, a necessary requirement for economical use, led to longer root lengths. Furthermore, we observed that the nitrogen uptake per unit average flow power was higher for the F/NF configuration compared to continuous flow. Consequently, we infer that in hydroponic cultivation, altering the flow configuration to a F/NF type could be more cost-effective with less nutrient solution wastage, promoting better plant root growth compared to a continuous flow scenario.

We investigate computationally the transport characteristics for flow of MWCNT-Fe3O4/H2O hybrid nanofluid through a wavy channel under the influence of an externally applied magnetic field. The flow and temperature fields are analyzed in terms of streamlines, isotherms, average Nusselt number ((Formula presented.)), magnetic enhancement ratio (ERm), and magnetic performance factor (PFm) for the following range of parameters: 100 (Formula presented.) Re (Formula presented.) 500, 0 (Formula presented.) Ha (Formula presented.) 10, and 0% (Formula presented.) 0.3%. The strength of the reverse flow in the recirculatory zones decreases with Ha, and beyond a critical Ha, the flow becomes attached even in the diverging part of the channel. The hot spot intensity near the walls decreases and hence, the value of (Formula presented.) increases with the increase in volume fraction of nano-particles and Ha. The rate of increment of (Formula presented.) is steeper at lower values of Ha. It further reveals that PFm monotonically decreases with Ha for lower Re (= 100). For higher values of Re, PFm decreases with Ha for its lower and higher values, while for the intermediate range of Ha, PFm increases with Ha.

Viscoplastic fluids flow through a microfluidic channel having a built-in two-part cylinder inside, while the upstream and downstream parts of the cylinder bear the surface potential of the same sign but of different magnitudes. We consider the Herschel-Bulkley model in describing the rheology of the viscoplastic fluids considered in this analysis. Consistent with the finite element method, the modeling framework employed here considers the prevailing effect of fluid rheology, and geometrical configuration-modulated electroosmotic forcing while solving the transport equations governing the mixing dynamics. We demonstrate that electroosmotic forcing, induced from the topology-modulated electrical double-layer effect, upon interacting with the prevalent viscous force in the field, leads to the flow reversal in the region closer to the built-in cylinder, which in turn, gives rise to the formation of vortices therein. As seen, the shear-thinning nature of the viscoplastic fluid results in an enhancement of the recirculation velocity strength, albeit the inevitable yield stress of the fluid sparsely influences the onset of flow recirculation. By showing the impact of the geometrical parameter of the cylinder and viscoplastic effect (signifying the effect of yield stress) on the recirculation strength, we show that the developed vortices in the pathway promote mixing of the constituent fluids nontrivially. Also, the characteristic time for shear-induced binary aggregation that illustrates the underlying mixing of fluids containing biomolecules, such as proteins and DNAs, is calculated based on the maximum strain rate. It is seen that cylinder radius and flow behavior index strongly affect the shear-induced binary aggregation kinetics and the associated probability density distribution of particles, while the yield stress has a negligible impact on the same.

We analytically investigated the electroosmotic flow characteristics of complex viscoelastic liquids within a charged hydrophobic microchannel, considering the pH and salt concentration-dependent surface charge effects in our analysis. We examined the variation of the electric-double layer (EDL) potential field, the surface charge-dependent slip (SCDS) length, the flow field, the viscosity ratio, and both normal and shear stresses in relation to the bulk pH, bulk salt concentration, and Deborah number of the solution. Our current findings indicate that, under strong flow resistance due to increased electrical attraction on counter ions, a highly basic solution with a high EDL potential magnitude results in a significant decrease in the slip length. Neglecting the effect of SCDS leads to an overestimation of flow velocity, with this overprediction being more pronounced for highly basic solutions. This overestimation diminishes as bulk salt concentration increases, particularly when compared to strongly acidic solutions. Furthermore, a noticeable increase in average velocity is observed as the Deborah number rises for highly basic solutions compared to highly acidic ones. This is attributed to the substantial reduction in apparent viscosity caused by the shear-thinning nature of the liquid at higher shear rates, supported by a larger zeta potential modulated strong electrical force for basic solutions. Additionally, we found that the intensity of shear and normal stresses tends to increase with bulk pH, primarily due to the rise in electric body force at higher zeta potential. These results can potentially inform the design and development of a compact, nonmoving electroosmotic pump for transporting biological species with varying physiological properties, such as solution pH. This technology could be applied in subsequent processes involving mixing, separation, flow-focusing for cell sorting, and other related applications.

The current study employs porous metallic blocks to quantitatively explore the characteristics of conjugate heat transport within the wavy solar power plant. Modelling of the flow field within the porous block is done using the Darcy-Brinkman-Forchheimer framework. By employing the boundary conditions, which are consistent with the practical applications, the governing equations are numerically solved for the transport variables. The current work highlights variations in the average Nusselt number, performance factor, temperature field, and conductive heat flux for a window of Reynolds and Darcy numbers. It is anticipated that the intensity of the conductive heat flow will significantly decrease with an increase in Reynolds numbers in its smaller range. The percentage increase in the average Nusselt number when using porous metallic blocks, compared to a porous blockless channel, is estimated to be in the range of 3.3 % to 83.95 % for the examined range of Reynolds numbers. Additionally, the average Nusselt number is underestimated, ranging from 874.17 % to 181.9 %, when considering channels with wall thicknesses half of the channel inlet height within the examined Reynolds number range. As can be shown, the performance factor rises monotonically with the Reynolds number and exceeds unity for increasing Darcy number beyond a critical Reynolds number. Additionally, for lower and higher Reynolds number values, the different influence of wall thickness and its thermal conductivity on performance factor has been predicted. The conclusions drawn from this work seem to be useful for the construction of economical solar plant largely used in many industrial applications as well as for the design of other devices used for effective thermal management of heat.

In light of the Joule heating impact, the goal of this work is to examine how electrical conductivity affects the electroosmotic flow characteristics inside wavy microchannels. Leveraging the COMSOL Multiphysics software, thereby a numerical model has been designed to calculate the underlying temperature, potential, and flow fields. Additionally, the experimental findings in the limiting scenario validate the numerical model. Employing a range of physically logical variables for the wavy wall dimensionless amplitude, liquid's reference electrical conductivity, and reference external electric field, we deeply examined the external electric field, conductive heat lines, flow field, maximum temperature rise, and average flow velocity. Both the electroosmotic flow velocity and the conductive heat flux intensity have been identified to be more intense at bigger amplitudes of the wavy microchannel owing to the enhanced electric field strength located in the throat. An increase in the conductive heat flux intensity, which allows for an increase in the flow velocity magnitude, is brought about by an increase in the liquid's reference electrical conductivity. As the reference electrical conductivity and electric field intensity increased, it became apparent that the maximum temperature rise also increased. Nevertheless, the same reduces as the wavy wall's amplitude increases. In response to an intensification in electrical conductivity, the average flow velocity only increases when the reference electric field intensity is high, from 25000 to 50000 V/m. Moreover, as the wave amplitude expands, the flow velocity decreases. Designing an electrical force-driven flow manipulator that produces heat through Joule heating can benefit from the insights drawn from this work.

The ionic characteristics and current rectification are investigated within a diverging nanochannel containing positively-negatively (PN) charged grafted porous polyelectrolytes, in this work. The underlying transport equations are numerically solved. The ionic selectivity as well as the associated transference number, net current output, rectification factor, and potential field are analysed by altering the bulk ionic concentration and bulk pH of the KCl ionic solution. A non-uniform electric field intensity is found in the diverging section of the nanochannel. It becomes apparent that the cationic concentration is higher in the acidic type of solution. The nanochannel is shown to be cationic selective for the acidic solution. The rectification factor is found to be much greater than unity when a diverging PN type nanochannel is employed. For the basic kind of solution, the rectification factor is found to be larger. The largest rectification factor has been determined to be up to 93.8 for bulk pH equal to 10. Therefore, the outcomes from this work are useful in designing effective current rectification devices.

We explore the pH-sensitive electrical energy generation in a salinity gradient utilizing a bio-inspired nanochannel. The underlying transport equations have been solved numerically using a commercial software based on the finite-element technique. A methodical examination of the space charge density of the PEL, EDL potential field, cationic concentration, maximum pore power, and the maximum energy conversion efficiency has been carried out for a range of the permittivity ratio of the PEL to the electrolytic layer and the pH-level of the right-side reservoir. It reveals that the space charge density magnitude inside the PEL decreases due to the basic character of the solution and the ion-partitioning effect cause. In addition, when the solution is acidic, the bio-inspired nanochannel is shown to generate the maximum pore power up to 99.51–133.62% higher than the simple nanochannel. Because of the smaller PEL space charge density magnitude, both the plane and bioinspired nanochannels produce lesser power generation and maximum efficiency for the basic kind of solution. The inferences made from the present study may lead to the design and development of high density energy-generating devices.

This study explores electroosmotic mixing in microfluidic channel with predefined surface topology, mainly focusing the effect of surface charge-dependent slip length on the underlying mixing dynamics. Our analysis addresses the need for precise control of flow and mixing of the participating fluids at microscale, crucial for medical and biomedical applications. In the present work, we consider a wavy microchannel with non-uniform surface charge to explore the electroosmotic mixing behavior. To this end, adopting a finite-element approach, we numerically solve the Laplace, Poisson-Boltzmann, convection-diffusion, and the Navier-Stokes equations in a steady-state. The model is validated by comparing the results with the available theoretical and experimental data. Through numerical simulations, the study analyzes electroosmotic flow patterns in microchannels, highlighting the impact of surface charge-dependent slip lengths on mixing efficiency. For example, at a diffusive Peclet number of 200, mixing efficiency drops from 95.5% to 91.5% when considering surface charge-dependent slip length. It is established that the fluid rheology, characterized by Carreau number and flow behavior index, non-trivially influences flow field modulation and mixing efficiency. Increased Carreau numbers enhance flow velocity, affecting overall mixing of the constituent fluids in the chosen fluidic pathway. For instance, by increasing the Carreau number from 0.01 to 1.0, a discernible trend emerges with higher flow line density and accelerated velocity within the microchannel. The study also examines the effect of diffusive Peclet numbers on the mixing efficiency, particularly in the convective regime of underlying transport. These insights offer practical guidance for designing microfluidic systems intended for enhanced mixing capabilities. Additionally, the study explores the likelihood of particle aggregation under shear forces, vital in biological non-Newtonian fluids, with implications for drug delivery, diagnostics, and biomedical technologies.

The initial emergence of the primary root from a germinating seed is a pivotal phase that influences a plant's survival. Abiotic factors such as pH, nutrient availability, and soil composition significantly affect root morphology and architecture. Of particular interest is the impact of nutrient flow on thigmomorphogenesis, a response to mechanical stimulation in early root growth, which remains largely unexplored. This study explores the intricate factors influencing early root system development, with a focus on the cooperative correlation between nutrient uptake and its flow dynamics. Using a physiologically as well as ecologically relevant, portable, and cost-effective microfluidic system for the controlled fluid environments offering hydraulic conductivity comparable to that of the soil, this study analyzes the interplay between nutrient flow and root growth post-germination. Emphasizing the relationship between root growth and nitrogen uptake, the findings reveal that nutrient flow significantly influences early root morphology, leading to increased length and improved nutrient uptake, varying with the flow rate. The experimental findings are supported by mechanical and plant stress-related fluid flow-root interaction simulations and quantitative determination of nitrogen uptake using the total Kjeldahl nitrogen (TKN) method. The microfluidic approach offers novel insights into plant root dynamics under controlled flow conditions, filling a critical research gap. By providing a high-resolution platform, this study contributes to the understanding of how fluid-flow-assisted nutrient uptake and pressure affect root cell behavior, which, in turn, induces mechanical stress leading to thigmomorphogenesis. The findings hold implications for comprehending root responses to changing environmental conditions, paving the way for innovative agricultural and environmental management strategies.

We investigate energy generation from salinity gradients inside a nanopore that is connected to reservoirs at both ends. We consider that the inner wall surfaces are grafted with a densely grafted polyelectrolyte layer (PEL). We developed the PEL grafting density-dependent correlation of dielectric permittivity, molecular diffusivity, and dynamic viscosity in this endeavor. Using these correlations, we employ the finite element framework to solve the equations describing the ionic and fluidic transport. We use a partially hydrolyzed polyacrylamide polymer solution, which exhibits a shear-thinning fluid, in combination with the KCl electrolyte for energy-harvesting analysis. To describe the shear-rate-dependent apparent viscosity of non-Newtonian liquid, we have employed the Carreau model. For a window of right-side reservoir concentration, we investigate the effects of ion-partitioning in conjugation with the change in PEL grafting density on the ionic field, ionic selectivity, pore current, osmotic power, energy conversion efficiency, and flow field. The findings of this endeavor demonstrate how the ion-partitioning effect lowers the screening effect and raises the electrical double layer (EDL) potential by reducing the counterions in PEL. We show that the unique distribution of the ionic field leads to a higher prediction of generated osmotic power and power density due to the ion-parting effect. Additionally, we establish that the augmentation in PEL space charge density leads to improvement in average flow velocity, osmotic power, and consequently energy conversion efficiency. We establish that the generated osmotic power density and the energy conversion efficiency become very high at the higher grafting density. In summary, inferences of this analysis are deemed pertinent in designing the nanoscale device intended for high and efficient osmotic energy generation.

This study introduces an innovative Grade 1 paper-based microfluidic device designed for the rapid, sensitive, and cost-effective detection of methanol in alcoholic beverages. The device integrates chemical reagents and sample fluid on a single paper strip, facilitating a straightforward and portable testing mechanism. The detection of methanol is achieved through a colorimetric reaction involving potassium permanganate, sulfuric acid, sodium bisulfite, and chromotropic acid. Upon interaction with methanol, the reagent mixture produces a distinct color change to purple, which can be visually assessed or quantified. The device works well with small sample volumes (usually less than 50 μl), making it ideal for field applications with minimal resources. The experimental validation confirmed that the device can detect methanol concentrations ranging from 5% (v/v) to 30% (v/v). This range of detection encompasses the critical concentrations found in contaminated alcoholic beverages responsible for methanol poisoning. In addition, numerical simulations were conducted at various time intervals for methanol concentrations, leading to the development of a colorimetric index specifically for measuring alcohol concentration ranging from 5% to 30% (v/v). Furthermore, experiments on both branded and locally made alcoholic beverages validated the accuracy of our developed colorimetric index. This paper-based technology provides various benefits compared to conventional methods, such as lower expenses, simplicity of operation, and the possibility of large-scale manufacturing and distribution in areas with limited resources.

We experimentally investigate the effect of lead (Pb2+) contamination on the roots of an Assamese rice line variety Lachit using a heavy metal analyzing fluidic tool. To demonstrate the adverse effects of lead contamination on rice seedlings in a controlled environment, we have performed a number of multidisciplinary experiments. Also, we develop a numerical model in this endeavor to predict the Michaelis-Menten kinetics parameters, which are used to depict the lead transport phenomenon following soft root structure-media flow interactions. We show that increased inlet lead concentration of the media solution leads to a reduction in root growth exponentially in the developed fluidic device. As supported by the Raman spectra analysis, the drastic metabolic changes are visible under lead contamination. Our results revel that, in comparison to the control condition, lead accumulation results in a decrease in the uptake of nitrogen and also, the metallic nutritional components (K+, Na+, and Ca2+). Under lead contamination, the average osmotic pressure difference at the root surface is seen to be less than in the control situation. The inferences drawn from the current research shed light on the detrimental effects of lead contamination on rice roots, which have the potential to significantly lower agricultural yields and threaten food security in areas where rice is the primary food source.

In the current study, forced convective conjugate heat transfer of non-Newtonian fluids has been examined in a wavy solar power plant with integrated metallic porous blocks. The associated flow and temperature fields were estimated numerically using the finite-element method-based solver employing the Darcy-Brinkmann-Forchheimer framework. Also, the results of existing theoretical and experimental studies are employed to validate the current numerical model. The flow field, heat lines, average Nusselt number, and thermo-hydraulic performance factor were thoroughly investigated by varying the flow behaviour index, Darcy number, and thermal conductivity ratio of the solid to fluid. As explored in the current endeavour, fluid rheology and permeability of the porous block modulate the flow field which in turn improves the heat transfer rate as well as performance factor. For applications involving heat exchange in solar heating, the current findings will be beneficial.

Blue energy generation in nanochannels based on salinity gradients is currently the most promising method in the area of nonconventional energy production. We used a semidiluted pure sodium carboxymethylcellulose (NaCMC)-KCl aqueous solution to study the characteristics of blue energy generation within a charged nanochannel. We solve the corresponding equations for ionic transport using a numerical technique based on the finite element method. Our analysis focused on the electric double layer (EDL) potential field, open circuit current, diffuse potential, electric conductance, maximum generated pore power, and maximum energy conversion efficiency by varying concentrations of the salt in the left-side reservoir and the bulk polyelectrolyte. The results indicate that as the polyelectrolyte concentration increases, the extent of EDL overlap considerably reduces. With an increase in polyelectrolyte concentration, the open circuit current increases, while the diffuse potential reduces. It was observed that both electrical conductance and maximal pore power improve considerably with higher polyelectrolyte concentrations. Interestingly, our modeling framework demonstrates a power density substantially higher (up to 16.31 W/m2) than earlier configurations and surpasses the established commercial limit (5 W/m2). Furthermore, our findings reveal that the reservoir salt concentration significantly affects the rate of decline in the maximum energy conversion efficiency as the polyelectrolyte concentration increases. The research paves the way for the development of high-power-density devices with several practical applications.

We examined the thermo-hydraulic characteristics for conjugate heat flow in the solar power plant having wavy channel with porous blocks (WCPB), while taking the thermal dispersion effect into account. The flow field inside the porous blocks is modelled using the Darcy–Brinkman–Forchheimer equations and the finite element method-based solver to solve the transport variables numerically. The temperature field, conductive heat flux, local Nusselt number, average Nusselt number and performance factor has been examined by changing the thermal dispersion coefficient, Reynolds number and Darcy number. We found that the average temperature decreases and conductive heat flux enhances by thermal dispersion near the bottom wall close to porous blocks. The rate of increase in average Nusselt number and performance factor with increase in dispersion coefficient is seen to be higher at the higher Reynolds number. It's interesting to note that the average Nusselt number underestimated with greater extent at higher dispersion coefficients as a result of ignoring the conjugate heat transfer effect. Moreover, the performance factor with the higher Reynolds number (= 500) is found to be more than unity. Also, when Reynolds number is 500, the performance factor for WCPB becomes larger than the plane channel with pours block at higher dispersion coefficient and Darcy number. The results of this analysis suggest that the proposed system is cost-effective to be used in the solar power plant.

This study describes a numerical analysis on blue energy generation using a charged nanochannel with an integrated pH-sensitive polyelectrolyte layer (PEL), considering ion partitioning effects due to permittivity differences. The mathematical model for ionic and fluidic transport is solved using the finite element method, and the model validation is performed against existing theoretical and experimental results. The study investigates the influence of electrolyte concentration, permittivity ratio, and salt types (KCl, BeCl2, AlCl3) on the energy conversion process. The findings illustrate the substantial role of ion partitioning in modulating ionic concentration and potential fields, thereby affecting current profiles and energy conversion efficiencies. Remarkably, overlooking ion partitioning leads to significant overestimations of power density, highlighting the necessity of this consideration for accurate device performance predictions. This work introduces a promising configuration that achieves higher power densities, paving the way for the next generation of efficient energy-harvesting devices. The findings offer valuable insights into the development of state-of-the-art blue energy harvesting nanofluidic devices, advancing sustainable energy production.

Using positively charged patches embedded in the walls of a microreactor, we generated electroosmotic vortices to analyze chemical reactions involving the flow of viscoplastic species. Reactant species A and B undergo a reaction to produce species C, which possesses physical properties suitable for biomedical applications. We developed a modeling framework, extensively validated with the available experimental results as well, to solve relevant transport equations considering pertinent boundary conditions. By varying parameters, such as the Bingham number, diffusive Peclet number, relative concentration of species B, flow-behavior index, and Damkohler number within physically justified ranges, we examined the flow field, species concentration, average product concentration, and generated species flow rate. Our findings indicate that the liquid yield stress and shear-thinning nature strongly influence vortex strength and the structure of yielded and unyielded regions. Notably, electroosmotic vortices enhance product species concentration compared to cases without vortices across the chosen range of diffusive Peclet numbers, providing convective mixing strength for reactants. For lower Bingham number values, product concentration trends increase then decrease with increasing Peclet numbers, whereas for higher Bingham numbers, it exhibits a monotonic decrease. Additionally, lower Bingham numbers lead to increased average product concentration as flow-behavior index decreases, while higher Bingham numbers show the opposite trend. Furthermore, average product concentration increases up to critical Damkohler number values for smaller Bingham numbers but becomes insensitive to Damkohler number changes with greater Bingham numbers. These insights of our analysis pave the way for designing innovative, highly effective microreactors largely used for biochemical and biomedical applications.

In this article, thermal–hydraulic performance and entropy generation (EG) characteristics for pressure-driven flow in a wavy channel with linearly varying amplitude (LVA) at the entrance region are computationally investigated. The computational simulations have been conducted for a wide range of Reynolds number 5 ≤ Re ≤ 1000 and normalized entrance length (EL) of LVA 0 ≤ EL ≤ 25.5. The results reveal that the flow field and heat transfer rate for the wavy channel with varying amplitude are remarkably different from those for a wavy channel (WC) with uniform amplitude, and the characteristics can be modulated by varying EL. The reversal of flow takes place in the wavy passages beyond a threshold value of Re, and the number of recirculating zones and the strength of the flow reversal strongly depend on EL. The average Nusselt number for the present WC is more than that of the plane channel (PC) after a critical value of Re only and at Re = 1000, the enhancements in average Nusselt number as compared to the plane channel are 6.91%, 20.67%, 26.37%, and 36.54%, for EL = 25.5, 11.5, 5.5, and 0, respectively. The combined influences of the augmentation in the average Nusselt number and the frictional pressure drop are presented in terms of performance factor (PF), which consistently decreases with the increase in Re for all non-zero EL, and the decrement is steeper for lower Re values. The average total entropy generation (EG) for WC is lower than PC at higher Re values, and the maximum percentage decrease in average total EG for WC compared to PC is achieved for EL = 11.5 at Re = 1000.

We have numerically investigated the electrodiffusio-osmotic (EDO) transport of non-Newtonian electrolytic solution, governed by an externally applied electric field and concentration difference, in a charged nanochannel connected with two reservoirs. We have examined the EDO transport characteristics by varying electrical, chemical, and rheological parameters. The relative augmentation in net throughput due to EDO transport is compared to the pure electro-osmotic flow and is found to be greater than unity [reaches up to the order of ∼O(103)] for the considered range of concentration difference and flow-behavior index. As shown, the EDO throughput with concentration difference follows an increasing-decreasing trend at the smaller nanochannel height (<10 nm), while exhibiting an increasing trend at the higher nanochannel height (>10 nm). Notably, the net flow for shear-thinning fluid gets fully reversed at higher concentration differences and for a higher value of zeta potential. In the second part of the work, we discuss the use of an artificial neural network (ANN) essentially to predict the net EDO throughput from the nanochannel. The ANN model considered here is of a single-hidden-layer feedforward type. For activation, we used a sigmoid-purelinear transfer function between the layers. Additionally, the Levenberg-Marquardt algorithm is used to perform the backpropagation. To predict the volume flow rate per unit width, we have used four input features: concentration difference, flow-behavior index, nanochannel height, and zeta potential. We have established that an ANN model with eight neurons in the hidden layer accurately predicts the flow rate per unit width with a very small root mean squared error. The inferences of this analysis could be of huge practical importance in designing the state-of-the-art nanodevices/systems intended for offering finer control over the underlying transport.

A theoretical model for entropy generation for an electroosmotic flow through a rectangular microchannel considering the finite size of ions and interfacial slip has been developed in this work to offer physical insights into the contributors of entropy generation. We use the Navier-slip model to represent interfacial slip and the modified Poisson–Boltzmann equation to describe the finite size of ions on the electric double-layer potential distribution without Debye–Huckel linearization. The modified Poisson–Boltzmann and the conservation of mass, momentum, and energy equations have been numerically solved using a finite element method-based solver. The numerical model is extensively validated with the reported experimental and numerical works. Results are presented for different viscous dissipation, Joule heating, Debye parameter, thermal Peclet number values, steric factor, and slip coefficient. It reveals that the effect of the finite size of ions on entropy generation with the consideration of interfacial slip strongly depends on the strength of the viscous and Joule heating. The average total entropy generation decreases with the slip coefficient, while it increases with the steric factor for lower values of thermal Peclet number (Pe). In contrast, the effect is opposite at higher values of Pe. For Pe = 0.1, the decrements in average total entropy generation are found as 45.25%, 38.42%, 34.89%, and 32.45%, respectively, for the steric factor of 0, 0.1, 0.2, and 0.3 with a slip coefficient of 0.1 as compared to without slip and point ion charge. For Pe = 2, the corresponding increments in average total entropy generation are found as 39.72%, 27.26%, 22.55%, and 19.69%, respectively.

We have investigated the role of viscoelectric effect on diffusioosmotic flow (DOF) through a nanochannel connected with two reservoirs. The transport equations governing the flow dynamics are solved numerically using the finite element technique. We have extensively analyzed the variation of induced field due to electric double layer (EDL) phenomenon, relative viscosity as modulated by the viscoelectric effect as well as reservoir's concentration difference, and their eventual impact on the underlying flow characteristics. It is revealed that the induced electric field in the EDL enhances fluid viscosity substantially near the charged wall at a higher concentration. We have shown that neglecting viscoelectric effect in the paradigm of diffusioosmotic transport overestimates the net throughput, particularly at a higher concentration difference. Furthermore, we show that pertaining to chemiosmosis dominated regime, the average flow velocity modifies with the increase in concentration difference up to a critical value. In comparison, the rise in the strength of resistive electroosmotic actuation by the accumulation of anions in the upstream reservoir reduces the average flow velocity at a higher concentration difference. We have reported a reduction in critical concentration with the increase in viscoelectric effect. The inferences of this analysis are deemed pertinent to reveal the bearing of viscoelectric effect as a flow control mechanism pertaining to DOF at nanoscale.

Purpose: The purpose of this paper is to analyze the heat and momentum transfer for steady two-dimensional incompressible nanofluid flow through a wavy channel with linearly varying amplitude in the entrance region. Design/methodology/approach: The mass, momentum and energy conservation equations for laminar flow of Cu-water nanofluids are computationally solved using the finite element method. A parametric study is carried out by varying the dimensionless length of the channel section with varying amplitude (EL), Reynolds number (Re) and nanoparticle volume fraction (Φ) in the ranges 0 ≤ EL ≤ 25.5, 105 ≤ Re ≤ 900 and 0 ≤ Φ ≤ 0.04. Findings: A higher heat transfer rate is seen in the wavy channel compared to a plane channel beyond a critical value of Re (Recrit) whose value varies with EL; moreover, the overall heat transfer decreases with EL. The heat transfer rate increases with phi for all EL values investigated. The combined effects of the increase in the overall heat transfer and the associated pressure drop in the wavy channel compared to the parallel plate channel are presented as performance factor (PF) against EL. For the highest value of EL (= 25.5), PF monotonically decreases with Re. For smaller values of EL (= 5.5 and 11.5) and also for EL = 0, PF decreases with Re in the lower and the higher Re regimes, while it increases in the intermediate Re regime. In all cases, PF is higher for φ = 0.04 than for the base fluid. The sensitivity of the average Nusselt number to nanoparticle volume fraction follows a non-monotonic trend with the change in Re, φ and EL. Practical implications: This study finds relevance in several applications such as solar collectors, heat exchangers and heat sinks. Originality/value: To the best of the authors’ knowledge, the analysis of forced convection flow of nanofluid through a wavy channel with linearly varying amplitude is reported for the first time in the literature.

Purpose: The purpose of this paper is to analyze numerically forced convective conjugate heat transfer characteristics for laminar flow through a wavy minichannel. Design/methodology/approach: The mass and momentum conservation equations for the flow of water in the fluidic domain and the coupled energy conservation equations in both the fluid and solid domain are solved numerically using the finite element method. The exteriors of both the walls are subjected to a uniform heat flux. Findings: The results reveal that the theoretical model without consideration of the effect of wall thickness always predicts a lower value of average Nusselt number ((Formula presented.)) as compared to the case of conjugate analysis, although it varies with the thickness as well as material of the wall. For the low amplitude of the wall (α = 0.2), the performance factor (PF) becomes very high for Re in the regime of 5 (⩽) Re (⩽) 15. For any geometrical configurations, conjugate heat transfer analysis predicts higher PF as compared to that of nonconjugate analysis. Practical implications: The present study finds relevance in several applications, such as solar collectors and heat exchangers used in chemical industries and heating-ventilation and air-conditioning, etc. Originality/value: To the best of the authors’ knowledge, the analysis of combined influences of the thickness and the material of the wall of the channel together with the geometrical parameters of the channel, namely, amplitude and wavelength on the heat transfer and fluid flow characteristics for flow through wavy minichannel in the laminar regime is reported first time in the literature.

We investigate the heat transfer and flow characteristics for an electroosmotic flow of Carreau fluid through a wavy microchannel, considering the finite size of ions i.e., steric effect. The flow of electrolytic liquid is considered steady, two-dimensional and incompressible. The modified Poisson-Boltzmann equation, Laplace equation, continuity equation, momentum equation, and energy equation are solved numerically using a finite element method-based solver. The computed flow and temperature fields are validated by comparison with published results. The flow and temperature fields and average Nusselt number are computed by varying the steric factor, Weissenberg number, dimensionless amplitude and Brinkman number in the following ranges: 0 ≤ ν ≤ 0.3, 0.01 ≤ Wi 1, 0.1 ≤ α ≤ 0.5 and 10−5 ≤ Br ≤ 10−3, respectively. We found the locations of the local maxima and minima of Nusselt number at the convex and concave surfaces of the channel for a lower Brinkman number (=10−5). In contrast, the corresponding locations are swapped at higher Brinkman number (=10−3). The value of average Nusselt number increases with the increase in Weissenberg number and decreases with the steric factor for the smaller Brinkman number (=10−5). Whereas, it decreases with Wi for non-zero values the of steric factor with higher Brinkman number (=10−3). Moreover, the increase in amplitude enhances the average Nusselt number at higher Brinkman number (=10−3).

In the present work, the thermo- hydraulic characteristics are studied for a laminar viscoplastic flow through raccoon and serpentine type wavy channels. The results are presented by varying Bingham number (Bn), power-law index (n), Reynolds number (Re), dimensionless amplitude, and wave number in the physically justified ranges. It is found that the size of the recirculatory zone decreases with Bn and the zone disappears at the higher Bn values. The topology of the yielded-unyielded region highly depends on the geometry and the range of Bn. Moreover, the value of average Nusselt number decreases with n. With the increase in Bn, average Nusselt number gradually decreases up to a critical Bn value and then increases sharply at higher Bn values. Interestingly, the wavy channel is only advantageous at smaller Bn values up to a critical limit. The variation of performance factor (PF) strongly depends on the combined effect of rheological and geometrical parameters. Besides, results for raccoon and serpentine channels are highly dependent on the ranges of amplitude, wave number, Bn, and n.

Purpose: The purpose of this paper is to investigate computationally the hydrothermal characteristics for forced convective laminar flow of water through a channel with a top wavy wall and a flat bottom wall having metallic porous blocks. Design/methodology/approach: The governing equations are solved computationally using a finite element method–based numerical solver COMSOL Multiphysics® for the following range of parameters: 10 ≤ Reynolds number (Re) ≤ 500 and 10–4 ≤ Darcy number (Da) ≤ 10–1. Findings: The presence of porous blocks significantly influences the heat transfer rate, and the value of local Nusselt number increases with the increase in Da. The value of the average Nusselt number decreases with Da for the top wall and the same is enhanced for the bottom wall of the wavy channel with porous blocks (WCPB). The value of the average Nusselt number for WCPB is significantly higher than that of the wavy channel without porous block (WCWPB), plane channel without porous block (PCWPB) and plane channel with the porous block (PCPB) at higher Re. For PCPB, the performance factor (PF) is always higher than that of WCWPB and WCPB for Da = 10–4 and Da = 10–3. Also, PF for WCPB is higher than that of WCWPB for higher Re except for Da = 10–4. Further, the value of for WCPB is higher than that of PCPB at Da = 10–2 and 10–1 at Re = 500. Practical implications: The current study is useful in designing efficient heat exchangers for process plants, solar collectors and aerospace applications. Originality/value: The analysis of thermo-hydraulic characteristics for laminar flow through a channel with a top wavy wall and a flat bottom wall having metallic porous blocks have been analyzed for the first time. Further, a comparative assessment of the performance has been performed with a wavy channel without a porous block, a plane channel without a porous block and a plane channel with porous blocks.

We investigate the mixing of soft biofluids in a narrow fluidic device under the influence of electroosmotic vortices generated by the patterned soft polyelectrolyte layers (PEL)-modulated electrical double effect. We numerically solve the transport equations that describe the solute mixing in the chosen configuration and estimate the shear-induced kinetics of binary aggregation in the deployed soft matter system. The prevailing interplay of forcings that stems from the fluid rheology and geometrical parameters of the PEL substantially affects the size and strength of the developed vortices, which, in turn, non-trivially modulate the underlying mixing strength. We aptly demonstrate in this endeavor that the higher shear-thinning behavior of the constituent components together with the larger extent of PEL's structure results in enhanced solute mixing (>90%). Additionally, we estimate the characteristic time of binary aggregation kinetics, which is particularly pertinent for analyzing the mixing of biofluids containing biomolecules, based on the set of parameters used in this analysis. The results reveal that increasing the shear-thinning behavior of solutes decreases the characteristic time of binary aggregation kinetics. Overall, the findings of this work seem to be of beneficial importance for the design and development of state-of-the-art on-chip devices intended for the augmented mixing of soft biofluids.

With a focus on biochemical applications and utilizing relevant physical properties, the current study numerically analyzes the impact of electroosmotic vortex and fluid rheology on the chemical reaction characteristics of species. This is achieved by installing integrated positively charged patches on the extended region of the microreactor with three inlets for injecting the reactants and generating the electroosmotic vortex. In order to produce species “C” in the extended region of the microreactor, it is presumed that reactant species “A” is injected through the upper and lower inlets and reactant species “B” is injected via the intermediate inlet. To solve the associated transport equations with appropriate boundary conditions, a thorough theoretical framework is developed. The results show that the ability of the reactant species to react is boosted when vortices form in the microreactor, increasing the convective mixing strength for reactant species. Furthermore, the fluid rheology significantly affects the reaction characteristics, which is a noteworthy finding. For fluids exhibiting a higher shear-thinning nature, the average concentration of the produced species follows an increasing-decreasing trend with the Carreau number. Additionally, it becomes apparent that the influence of the Damkohler number on the average generated species concentration is negligible at lower Carreau numbers, but it increases with the Damkohler number at higher Carreau numbers. The study also reveals that both rheological and chemical parameters have a substantial impact on the flow rate of product species. Overall, the findings of this investigation provide valuable insights for the development of technologically advanced electroosmotic microreactor capable of effectively generating the intended product species.

By varying the pH values (pHR) and types of salt solution, we investigate the salinity gradient-induced electrical and mechanical flow energies inside a reservoir-connected charged nanochannel with a grafted pH-sensitive polyelectrolyte layer (PEL) on the inner surfaces. The aqueous solutions of KCl, LiCl, BaCl2, BeCl2, AlCl3, and Co(en)3Cl3 salts are used as the working fluid in the current investigation. We examine the associated ionic transport and flow field, aiming to understand the underlying physics behind the generation of electrical and hydraulic energy through alterations in pHR and types of salt solution. Our results reveal that the PEL space charge density decreases with increasing pHR at lower values, while it remains almost insensitive to higher pHR values. The electrical conductance and maximum pore power of the Co(en)3Cl3 solution are significantly higher compared to salts with monovalent and divalent cations. Furthermore, the magnitude of these two parameters decreases with lower pHR and becomes insensitive to higher pHR values. The results illustrate that the maximum electrical energy conversion efficiency enhances with pHR, reaching its highest level for the Co(en)3Cl3 solution. We expect that the findings of the current work will have a significant bearing on the design and development of a state-of-the-art salinity gradient-based energy convertor as a potential candidate for renewable energy sources.

The charged nanochannel surface and pH-sensitive grafted polyelectrolyte layer (PEL) play a critical role in the design of devices aimed at controlling nanofludic flow. They enable the manipulation of ionic transport by influencing the electric-double (EDL) layers that overlap. Additionally, the viscoelectric effect, amplified by a strong EDL electric field, may enhance the activation energy and viscosity of liquids. Motivated by this, we conducted a numerical investigation using a finite element method-based solver, COMSOL, to examine the effects of the viscoelectric effect on concentration-gradient-driven chemiosmotic flow in a charged soft nanochannel with grafted pH-sensitive polyelectrolyte layer on the inner wall surfaces. It is important to note that the nanochannel is positioned between two reservoirs with different pH values and bulk-ionic concentrations. The PEL is sensitive to protonic association-dissociation due to the presence of carboxylic and amine groups in monomeric units. In our study, we comprehensively demonstrate variations in key variables characterizing the underlying flow. These variations include changing the solute concentration in the left side reservoir within the range of 0.1-5 mol m−3, adjusting the pH of the right-side reservoir (pHR) within the range of 3-10, and varying the viscoelectric coefficient. The viscoelectric effect significantly raises viscosity near the wall due to the stronger EDL electric field generated at the left-side reservoir resulting from the higher solute concentration. On the other hand, viscosity tends to decrease with lower pHR values and remains unaffected by changes at higher pHR values. The average flow velocity shows an increasing-decreasing pattern as the concentration of the right-side reservoir is enhanced. Additionally, the decrease in flow velocity becomes noticeably more pronounced with higher solute concentrations in the right-side reservoir when accounting for the viscoelectric effect. The findings of the present study have practical implications for novel nanofluidic devices, frequently employed in various engineering applications to control flow.

Pertaining to the mixing of the non-Newtonian Carreau fluid under electrokinetic actuation inside a plane microchannel, we propose a new design of micromixer that involves inserting a two-part cylinder bearing zeta potential of the same sign but different magnitude in the upstream and downstream directions. We numerically solve the transport equations to predict the underlying mixing characteristics. We demonstrate that a substantial momentum difference between the microchannel's plane wall and cylinder leads to the development of a vortex in the flow pathway, which in turn, enhances mixing substantially. As shown, for a fluid having a highly shear-thinning nature, the vortex-assisted convection mixing strength increases with diffusivity of the candidate fluids. Moreover, it is shown that for the higher shear-thinning nature of the candidate fluid, an increase in cylinder radius enhances mixing efficiency and flow rate simultaneously, resulting in a “quick and efficient” mixing condition. Additionally, the fluid rheology significantly alters the kinetics of shear-induced binary aggregation. Our findings show that the shear-induced aggregation characteristic time sharply increases with increasing shear-thinning behavior of the fluid.

For liquids used in biological applications, a smaller diffusion coefficient results in a longer mixing time. We discuss, in this endeavor, the promising potential of the AC electrothermal (ACET) effect toward modulating enhanced mixing of electrolytic liquids with higher convective strength in a novel wavy micromixer. To this end, we develop a modeling framework and numerically solve the pertinent transport equations in a three-dimensional (3D) configuration numerically. By benchmarking the developed modeling framework with the experimental results available in this paradigm, we aptly demonstrate the maximum temperature rise, flow topology, species concentration field, and mixing efficiency in the proposed configuration for a set of parameters pertinent to this analysis. We find that the maximum temperature increase in the wavy micromixer, owing to the electrothermal effect, is less than 10 K even for the higher strength of the applied voltage, implying nondegradation of biological substances within the liquid sample. We report that the formation of significant lateral flow closer to the electrodes leads to a highly three-dimensional ACET flow field, which has a significant impact on the mixing efficiency for the range of diffusive Peclet numbers considered. We also report that the wave amplitude of the mixer, when intervening with the diffusive Peclet number, strongly impacts the mixing efficiency. As witnessed in this endeavor, for the smaller diffusive Peclet number, the mixing efficiency increases with amplitude, while the effect becomes the opposite for the higher Peclet number. The results of this study seem to provide an adequate basis for the design of a novel micromixer intended for enhanced solute mixing in realistic microfluidic applications.

Capillary wicking in a thicker gel blot microfluidics paper has been investigated through a combination of an analytical framework, experiments, and numerical simulations. The primary objectives of this work are to investigate the concentration-dependent wicking process inside thicker microfluidic paper and to estimate the concentration-dependent permeability using both theoretical models and experimental data. An additional goal is to estimate the parameters for saturation-dependent flow modeling in thicker microfluidic paper. To comprehend the wicking phenomenon on thicker gel blot paper, a series of experiments employing aqueous food dye solutions at varying concentrations has been conducted. In order to calculate the temporal wicking length analytically, the Brinkman-extended Darcy equation is implemented. By modifying the permeability expression for a simple rectangular unidirectional fiber cell and pure liquid, the expression of effective permeability for the analytical framework has also been introduced. The concentrations of the food dye solutions appear to have a substantial influence on the wicking phenomenon. Effective permeability and wicking length have been found to follow a decreasing pattern at lower concentrations while both increase at higher values. Intriguingly, employing a microfluidics paper with a relatively greater thickness facilitates the visualization of the fluid front. This phenomenon is identified by the formation of an acute angle at intermediate time instants, while the fluid front angle assumes an angle nearly ∼90° during smaller and higher time instants. In order to evaluate the saturation-dependent capillary pressure and permeability, the empirical correlation of concentration-dependent Brooks and Corey parameters is additionally determined experimentally. These parameters are subsequently employed in numerical simulations to illustrate the saturation-dependent flow field using Richards’ equation. Furthermore, numerical simulations based on these estimated model parameters have been conducted, and it turns out that the saturation field has an excellent agreement with the experimental results. The results of the current study can be used to design low-cost paper-based diagnostic devices for usage in healthcare and environmental applications.

We have numerically investigated the natural convective heat transfer and entropy generation characteristic inside a wavy solar power plant filled with MWCNT-Fe3O4-water nanofluid using the finite element method. The simulated flow and temperature fields are investigated in terms of streamline contour, isotherm contour, local Nusselt number, average Nusselt number, dimensionless total entropy generation, and dimensionless average total entropy generation by varying the dimensionless amplitude of the wavy wall and nano-particle volume fraction. We reported that the presence of a wavy wall and the addition of nano-particles decreases the strength of recirculation developed in the flow field. Moreover, as seen from the analysis, an increase in the amplitude of the wavy wall and nano-particle volume fraction enhances the average Nusselt number. The entropy generation due to viscous dissipation is dominated for the considered value of the Rayleigh number. In addition, our results show that the increase in wave amplitude and nano-particle volume fraction reduces the average entropy generation. Inferences of this analysis are expected to have far ranging consequences to the optimum design of the solar power plant.

We investigate the mixing and hydrodynamic characteristics computationally for a pure electroosmotic flow of non-Newtonian fluid through a nonuniformly charged micromixer with obstacles arranged in staggered and inline orders. The constitutive behavior of the fluids is described by the power-law model. We present the results by varying the dimensionless zeta potential (|ζ|), Debye parameter (κ), and power-law index (n) in the range of 1 ≤ |ζ| ≤ 8, 0.5 ≤ κ ≤ 100 and 0.5 ≤ n ≤ 1.5, respectively. The mixing is strongly influenced by the rheology of the fluids and the formation of the recirculatory zones. For the overlapped EDL (κ = 0.5), mixing efficiency (ME) decreases with n for lower |ζ| values, while ME increases with n for higher |ζ| values for both the orientation of obstacles. When the obstacles are arranged in a staggered manner, the variation of ME with n follows a decreasing-increasing trend for the intermediate values of |ζ|. The value of ME is higher for the inline arrangement with overlapped EDL (κ = 0.5) and is close to 100%. For thinner EDL (κ = 100), the value of ME is higher for inline arrangement only for |ζ|= 1 and 0.5 ≤ n ≤ 0.6, and for all other cases, it is higher for staggered arrangement. The presence of heterogeneous charged surface always enhances the mixing and the enhancement is always higher for shear-thickening fluid and for the staggered order of the obstacles. The present design of electroosmotic micromixer handling with non-Newtonian fluids provides a higher mixing efficiency as compared to most of the existing designs available in the literature. The values of n, κ and |ζ| are identified for the micromixer with two orientations of the obstacles for quick and efficient mixing and the findings may be helpful to design an efficient micromixer for the point-on care diagnostic applications handling with of non-Newtonian fluids.

We investigate the flow and mixing characteristics for an electroosmotic flow through a wavy micromixer using surface charge heterogeneity. The Laplace equation for the external electric field, Poisson-Boltzmann equation for potential distribution, and continuity and momentum equations for fluid flow and species transport equation have been solved by imposing the appropriate boundary conditions using a finite element method-based numerical solver. The results are presented by varying the phase lag of sinusoidal zeta potential between the two walls (Δφ), Debye parameter (κ), geometrical wave number (n), dimensionless wall amplitude (α), and diffusive Peclet number (Pe). The results reveal that the phase lag has a strong confluence on the flow field and mixing performance together with other physicochemical parameters. The strength of primary flow as well as the size of the recirculation zones increases with Δφ and κ, and additional recirculation zones are formed in the core of the mixer for Δφ = 0. The value of mixing efficiency is close to 100% up to a critical value of Pe (PeCri), the value of which is greater for the nonuniformly charged surface potential with a nonzero phase lag. For thinner EDL (κ = 150), a fully mixed state based on 90% mixing is achieved up to higher values of Pe with a higher flow rate at Δφ = π/2 and π. Also, for Δφ = π/2, the mixing efficiency as well as the flow rate enhances with the amplitude of the channel walls for PeCri≤ Pe ≤323.5. Moreover, for Δφ = 0, the value of mixing efficiency increases with α for 786 ≤ Pe ≤1000 with a 9.17% decrement in the flow rate for the change in α from 0.05 to 0.25.

In this work, we investigate the hydrothermal characteristics for laminar forced convective flow of water through sinusoidal asymmetric wavy channel of three types: linearly increasing amplitude channel (LIAC), linearly decreasing amplitude channel (LDAC) and constant amplitude channel (CAC). The computed velocity and temperature fields are analyzed by varying the Reynolds number (Re) and slope (A) of the linearly varying amplitude in the following ranges: 5 ≤ Re ≤ 200 and 0.02≤ A ≤ 0.04. The value of average Nusselt number is almost independent on the geometry of the channel at lower values of Re and A. At higher Re values, the average Nusselt number is the highest for LIAC followed by LDAC, and CAC. The combined effects of heat transfer increase in the wavy channel compared to plane channel and the associated pumping power is assessed using performance parameter (PF). For lower Re values the highest PF is obtained for CAC. For higher values of Re the PF is the largest for LDAC at A = 0.02 and 0.03, and the value of PF for A = 0.04 is the highest for CAC.

Purpose: The purpose of this study is to analyze the thermal, hydraulic and entropy generation characteristics for laminar flow of water through a ribbed-wavy channel with the top wall as wavy and bottom wall as flat with ribs of three different geometries, namely, triangular, rectangular and semi-circular. Design/methodology/approach: The finite element method-based numerical solver has been adopted to solve the governing transport equations. Findings: A critical value of Reynolds number (Recri) is found beyond which, the average Nusselt number for the wavy or ribbed-wavy channel is more than that for a parallel plate channel and the value of Recri decreases with the increase in a number of ribs and for any given number of ribs, it is minimum for rectangular ribs. The performance factor (PF) sharply decreases with Reynolds number (Re) up to Re = 50 for all types of ribbed-wavy channels. For Re > 50, the change in PF with Re is gradual and decreases for all the ribbed cases and for the sinusoidal channel, it increases beyond Re = 100. The magnitude of PF strongly depends on the shape and number of ribs and Re. The relative magnitude of total entropy generation for different ribbed channels varies with Re and the number of ribs. Practical implications: The findings of the present study are useful to design the economic heat exchanging devices. Originality/value: The effects of shape and the number of ribs on the heat transfer performance and entropy generation have been investigated for the first time for the laminar flow regime. Also, the effects of shape and number of ribs on the flow and temperature fields and entropy generation have been investigated in detail.

We investigate the electroosmotic mixing characteristics for flow through a hydrophobic microchannel with interfacial slip dependent heterogeneous surface charge. A comprehensive theoretical framework is developed to solve the Poisson–Boltzmann equation for the induced potential within the electrical double layer, mass and momentum conservation equations for fluid flow, and species transport equation with appropriate boundary conditions. We identify two different flow regimes based on diffusive Peclet number such that in the first regime the value of mixing efficiency is almost 100% as the recirculation zones formed due to the non-uniform surface potential provide sufficient convection mixing and the flow rate enhances with the slip length. The critical value of Peclet number increases with both the slip length and Debye parameter. In the next regime the effect of interfacial slip is significant in altering the mixing performance and the mixing efficiency decreases both with the slip and Debye parameter. The patch surface potential modulates the flow rate and mixing performance and, in this context, different range of patch surface potential for the considered physicochemical parameters is identified for which both the flow rate and mixing efficiency enhances due to the interfacial slip.

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.

The micromixing of two fluids plays a vital role in lab-on-a-chip devices. For obtaining better mixing efficiency, we propose a micromixer using patchwise surface potential heterogeneity and wavy wall. We numerically investigate the hydrodynamic and mixing characteristics for flow through a microchannel with a straight top wall and wavy bottom wall. The primary flow is actuated by an external pressure-gradient and patches are placed at the top wall with positive zeta potential, such that the reversed electroosmotic actuation forms the recirculation zones close to the top wall. The streamlines, flow velocity, recirculation zone velocity, species concentration, flow rate, and mixing efficiency are investigated by varying the relative pressure-gradient strength, Debye parameter, zeta potential and wavy surface amplitude. Two different configurations are considered by placing the patches at the top wall, opposite to the peaks and valleys of the bottom wavy surface, respectively. It reveals that the recirculation zone velocity increases with the increase in both Debye parameter and surface amplitude, whereas it decreases with relative pressure-gradient strength near the patch surfaces. The flow rate decreases with the increase in zeta potential and we also identify the values of zeta potential for chocking of flow in the microchannel. It reveals that the mixing efficiency monotonically increases with surface amplitude, and the variation with zeta potential is non-monotonic. We also identify the range of zeta potential for which the value of mixing efficiency is higher than 90% for different configurations of the channel.

The effect of non-uniform heating on the heat transfer characteristics for electroosmotic flow through a microchannel has been investigated numerically. The temperature field and Nusselt number are studied by changing the normalized wavelength of non-uniform heat flux (γ) and thermal Peclet number (Pe ) in the range of 1.5 ≤ γ≤ 6 and 1 ≤ Pe ≤ 100, respectively. It is found that the intensity of maximum temperature reduces for non-uniform heating as compared to the uniform heating. The maxima of local Nusselt number increases with a decrease in the wavelength of the non-uniform heat flux. The critical Peclet number (Pec) is found such that average Nusselt number shows the monotonic and non-monotonic variation with γ.

We explore the heat transfer characteristics for forced convective flow of a Newtonian fluid through the wavy channel under the effect of non-uniform heat flux. The findings are presented for different values of Reynolds number (Re) and dimensionless wavelength of the non-uniform heating (γ) in the range of 100 ≤ Re ≤ 500 and 0.25 ≤ γ≤ 4, respectively. The non-uniform heating decreases the hot spot intensity in the circulatory flow zone and moreover it induces additional maxima of Nusselt number as compared to the constant heating case. The average Nusselt number for sinusoidal heating case is much more than the constant heating case for the smaller undulation of the non-uniform heating.

Purpose: The purpose of this paper is to analyze the thermal, hydraulic and entropy generation characteristics for the magneto-hydrodynamic (MHD) pressure-driven flow of Al2O3-water nanofluid through an asymmetric wavy channel. Design/methodology/approach: Galerkin finite element method is used to solve the governing transport equations numerically within the computational domain using the appropriate boundary conditions. The temperature and flow fields are computed by varying Reynolds number (Re), Hartmann number (Ha) and nano-particle volume fraction (ϕ) in the following range: 10 ≤ Re ≤ 500, 0 ≤ Ha ≤ 75 and 0 ≤ ϕ ≤ 5%. Findings: The formation of the recirculation zones in the wavy passages, the size of it and the strength of the vortices formed can be modulated by the application of the magnetic field. The overall heat transfer rate increases with Ha for all ϕ both for a lower and higher regime of Re although the enhancement is more for lower values of Re and nanofluids as compared to base fluid and for intermediate values of Re, the effect of a magnetic field is almost insignificant. The magnetic performance factor (PFmagnetic) decreases with Ha although the rate of decrement varies with Re. The increase ϕ also enhances PFmagnetic especially at lower and higher values of Re. The addition of nano-particle enhances the entropy generation at lower values of the Re, while the opposite effect is seen for higher values of Re. Practical implications: The present study has enormous practical relevance for the design of heat exchanger applied for solar collectors, process plants, textile and aerospace applications. Originality/value: The combined effects on the heat transfer rate and the associated pressure drop penalty due to the applied magnetic field for the flow of nanofluid through an asymmetric wavy channel have not been reported to date. The effect of the magnetic field on the formation of recirculation zones and hot spot intensity in the asymmetric wavy channel has been examined in detail. The PFmagnetic is investigated first time for the MHD nanofluid flow through a wavy channel.

We investigate the thermo-fluidic and entropy generation characteristics for electroosmotic flow through a hydrophobic microchannel with the consideration of viscoelectric effect. A closed form expression for the velocity is obtained from the analytical solution of the momentum and continuity equations together with the Poisson-Boltzmann equation and thereafter the temperature field is computed numerically. The flow velocity, flow rate, average Nusselt number, and average total entropy generation are computed by varying the slip coefficient, viscoelectric coefficient (f), Brinkman number (Br), and thermal Peclet number(Pe). Results reveal that the viscoelectric effect decreases the flow velocity and percentage decrement in flow rate due to the viscoelectric effect is larger for the slip case and reaches up to 40.09%. The value of the average Nusselt number decreases with f at lower value of Br, and the effect is opposite at higher values of Br. Although the heat transfer enhancement is more with the interfacial slip, the augmentation decreases with f and increases with Pe. The value of average total entropy generation decreases with the increase in f, and decrement is substantial at higher values of Br.

The mixing and flow characteristics are numerically investigated for an electroosmotic flow through a heterogeneous charged micromixer with obstacles both at the top and bottom walls arranged in inline and staggered order by varying the obstruction angle (θ). The results are presented by varying the Debye parameter (κ), magnitude of the zeta potential (|ζ|), and obstruction angle in the range of 10 ≤ κ ≤ 100, 1 ≤|ζ| ≤ 4, and 60° ≤ θ ≤ 120°, respectively. Results reveal that the strength of the recirculation zone is the highest for θ = 90° and it enhances with κ and |ζ|, and moreover, the strength is always higher for the staggered arrangement of obstacles as compared to the inline order. For inline arrangement of the obstacles, the value of mixing efficiency (ME) decreases with κ as well as |ζ| and the highest values are seen for θ = 90°. For the staggered arrangement of obstacles, the variation of ME with κ is not monotonic; rather, it strongly depends on |ζ| and θ. The flow rate increases with the increase in κ and it is the lowest for θ = 90° and importantly, the flow rate is always more for inline arrangements of the obstacles.

The use of hydrophobic surfaces in electrokinetic flows results in an intricate analysis due to the coupling of surface potential and interfacial slip which challenges their independent measurement. Thus, it becomes significant to consider the slip-dependent surface potential which can decouple the interfacial slip from the zeta potential. In this article, we develop an analytical model to investigate the heat transfer characteristics for combined electroosmotic and pressure-driven flow through a plane microchannel considering the slip-dependent zeta potential. We solve analytically the Poisson–Boltzmann (PB) equation, the mass, momentum and energy conservation equations for hydrodynamically and thermally fully developed flow with appropriate boundary conditions to obtain closed form expressions for the induced potential within the electrical double layer (EDL), the velocity and temperature profiles and the Nusselt number in terms of different physico-chemical parameters. The results reveal that interfacial slip-dependent surface potential has a strong influence on the thermal transport phenomenon along with other parameters, like Joule heating, applied pressure-gradient, electrokinetic parameter, slip length and viscous dissipation. The velocity in the core region is always under-predicted considering the slip-independent surface potential and the under-prediction is amplified for thinner EDL and pure electroosmotic flow. Beyond the critical values of the slip length, the consideration of the slip-independent surface potential in the paradigm of thermal transport dynamics for electrokinetic flows, over-predicts the Nusselt number and the over-prediction is amplified for thinner EDL. Moreover, a critical Brinkman number, Brk is also identified such that for Br < Brk, Nusselt number increases with Debye parameter, while the opposite effect is observed for Br > Brk. The relative enhancement in Nusselt number due to the interfacial slip increases with the applied pressure-gradient and slip length at smaller values of Brinkman number. Furthermore, the sensitivity of Nusselt number on slip is highly dependent on the Debye parameter, Brinkman number and applied pressure-gradient.

We investigate flow characteristics for an electroosmotic flow of viscoelastic fluids through a hydrophobic plane microchannel, considering the coupled effect of interfacial slip and zeta potential. We employ a simplified Phan-Thien-Tanner model to describe the constitutive behavior of the fluid. The governing equations are solved analytically to obtain electric double layer (EDL) potential distribution, flow velocity, flow rate, stresses, and viscosity. We have compared the obtained analytical flow field with the established theoretical and experimental works at the limiting cases. We demonstrate that ignoring the effect of the interfacial slip on zeta potential will lead to underprediction of the flow rate, and this underprediction is amplified with the increase in the Deborah number, decrease in the EDL thickness, and increase in the slip coefficient. Moreover, the relative flow rate augmentation by the rheological behavior strictly depends on the range of slip coefficients with the change in the EDL thickness. Accordingly, we have identified three regions of the slip coefficient. In addition, the viscosity near the wall decreases with the slip coefficient for the slip dependent zeta potential model. In contrast, the normal and shear stresses are augmented with the slip coefficient. Outcomes of the present investigation may help one to understand the enhanced flow behavior for the transport of complex fluids through a hydrophobic microchannel.

The present work numerically investigates the thermo-fluidic and entropy generation characteristics for laminar forced convective flow through wavy channel at different Prandtl number (Pr). Results are presented for the following range of parameters: Reynolds number 5 ≤ Re ≤ 200 , Prandtl number 0.72 ≤ Pr ≤ 100 , dimensionless amplitude 0.3 ≤ α≤ 0.7 and dimensionless wavelength 0.5 ≤ λ≤ 1.5. It is observed that with increase in Pr, the thickness of the thermal boundary layer at trough region decreases slowly for smaller Re, whereas at higher Re, the rate of decrement is higher. The average Nusselt number increases with Pr for all amplitude, wavelength and Reynolds number. The relative heat transfer enhancement compared to equivalent plane channel is presented in terms of enhancement ratio (ER), and it shows a non-monotonic variation of ER with Pr at lower Re and a monotonic one at higher Re. The combined alteration of rate of heat transfer and pressure drop as compared to plane channel is enumerated by performance factor (PF), and the variation of PF with Pr shows non-monotonic behaviour at lower Re and monotonic one at higher Re. The variation of PF shows non-monotonic variation with Re for higher Pr and for smaller wavelength, whereas it monotonically decreases for all Pr at higher wavelength. Thermal entropy generation contribution is higher over the viscous one for all the cases considered. The local thermal entropy generation distribution varies with Re, Pr and geometrical configuration of the channel. For smaller amplitude (α = 0.3), the total entropy generation is minimum in the considered range of Re and Pr.

We analyse the thermo-hydraulic performance and entropy-generation characteristics for laminar flow through triangular corrugated channel. Results are presented in terms of heat transfer, pressure drop and entropy generation for different values of amplitude of waviness of the channel, wavelength and Reynolds number in the range of 5–500. It is found that the rate of heat transfer is augmented with both Reynolds number and amplitude of the wall waviness, together with increase in pressure drop. The enhancement in heat transfer and pressure drop as compared to equivalent straight channel are also assessed by performance factor combining the enhancement in heat transfer and corresponding increase in pressure drop. There is an intricate interplay between the geometrical parameters of the channel and the flow parameters in dictating the performance factor. Thermal entropy generation is dominant over the fluid friction for lower Reynolds number. The total entropy generation increases rapidly up to critical Reynolds number (Recri), after which it either remains almost constant or decreases gradually, and moreover Recri depends on the wavelength of the channel. The outcomes of the present work may be helpful to design the efficient and economic thermal devices and systems.

We numerically analyze the mixing and pressure drop characteristics for flow through wavy micromixer of two geometrical configurations, namely raccoon and serpentine for different values of amplitude of the waviness of the mixer (α), wavelength of the waviness (λ), Reynolds number(Re) and Schmidt number(Sc). Three different flow regimes are identified depending on the parameters influencing the mixing index. The mixing index for both the raccoon and serpentine mixer is very close to unity in the first regime (0.1 < Re < Re*). Beyond Re* the mixing is better for raccoon mixer as compared to serpentine for any particular value of Re, amplitude and wavelength. In case of the absence or insignificant size of recirculation zone, beyond Re* the difference in mixing index between raccoon and serpentine mixer increases with Re, while the same decreases in presence of significant size of recirculation zone within the mixer. The pressure drop is always higher for raccoon mixer as compared to serpentine and moreover, the difference in pressure drop between raccoon and serpentine mixer increases with increase in Re. The best micromixer has been proposed based on the findings of the present analysis.

Array of micro pin fin heat sinks shows higher thermal efficiency in high heat flux and critical devices such as aerospace, microelectronic etc. In this work, an array of micro square pin fins has been designed and for this copper is selected as workpiece material. Moreover, a numerical investigation of thermal performances and mechanical behavior of the designed fins has been carried out. The effects of Reynolds numbers on velocity profile and heat transfer performance have also been studied. Additionally, the equivalent (von-Mises) stress along with the structural and total deformations have been observed at the desired pressure applied on the surface of the pin fins. Numerical simulations with similar parametric conditions have also been conducted on a plate having the same dimensions without fins, and a comparison has been made with a plate having micro-fins. It has been observed that the array of square micro pin fins gives a better thermal performance than that of without fins.

Numerical analysis has been performed to analyse the effect of non-uniform heating on heat transfer charecteristics for steady laminar flow through wavy channel. Heat transfer charecteristics has been analysed with different heat flux amplitude and phase difference of sinusoidal heat flux. We observe an intricate interplay between the amplitude and phase difference of heat flux profile on the thermal transport characteritics. The local heat transfer enhancement is highly sensitive with change in amplitude of the sinusoidal heat flux.. For zero phase difference of heat flux profile, all local minima are higher in comparesion with local minima of the corresponding reciprocal phase difference, while the decrease in local maxima is not monotonic. Decrease in amplitude of heat flux increases the average Nusselt number, while for same heat flux amplitude zero phase difference yields higher average Nusselt number.

Numerical experiments have been performed to investigate the thermo-fluidic transport characteristics for laminar flow through sinusoidal wavy walled channel. The heat transfer and pressure drop characteristics are assessed for two different channels, namely, raccoon and serpentine for different values of amplitude and wavelength of the wall waviness. Our results reveal that the dependence of heat transfer on the geometry of the wall is strongly influenced by the wavelength of the wall waviness. For lower values of wavelength, the rate of heat transfer is almost same for both the channel, while the heat transfer for raccoon channel is always more than that for serpentine channel for higher values of wavelength and the difference appears to be more prominent for larger values of amplitude of wall waviness and Reynolds number. Furthermore, with the deployment of a performance parameter combining the enhancement in heat transfer and corresponding increase in pressure drop, we assess the thermo-hydraulic performance of the two channels. In contrast to the heat transfer characteristics, our results indicate that the performance factor of a serpentine channel is always more than that of a raccoon channel. The results of the present investigation may be considered as a basis for selection of geometry of channel wall for design of compact heat exchangers.