Electroviscous Effect Research Articles

Analysis of Electroviscous Effect for Flow of Micropolar Fluids in a Nanochannel with Overlapping Electric Double Layers at High Zeta Potential.

Flows in nanofluidic channels under the influence of pressure gradient often lead to the overlapping of the electrical double layers (EDLs) augmenting the electroviscous effect. In this work, we analyze the electroviscous effect for the flow of a micropolar fluid in a parallel plate nanochannel, considering EDL overlapping and interfacial slip. Closed-form expressions of EDL potential, velocity, microrotation, yielded streaming potential, and volumetric flow rate are derived semi-analytically for high zeta potential without accounting for the Boltzmann distribution. We observe a significant change in streaming potential with inverse ionic Peclet number (R) for its lower values, and the range of streaming potential is more for thicker EDL. The micropolarity parameter does not have any influence on the streaming potential for weaker EDL overlapping at a lower R value. For thicker EDL, velocity decreases with the micropolarity parameter, while it increases drastically with interfacial slip. However, velocity shows a non-monotonic behavior with interfacial slip and micropolarity parameter for thinner EDL. The microrotation remains invariant with interfacial slip for thicker EDL, whereas its magnitude decreases with slip length for thinner EDL. Although the sensitivity of the flow rate on slip (Qs*) increases with R for thicker EDL, the behavior is non-monotonic for thinner EDL. Furthermore, Qs* varies non-monotonically with the micropolarity parameter at higher couple stress parameter values and vice versa. In fact, the volumetric flow rate is highly sensitive to slip for thicker EDL overlapping.

Analysis of electroviscous effects in electrolyte liquid flow through a heterogeneously charged uniform microfluidic device

Charge-heterogeneity (i.e., surface charge variation in the axial direction of the device) introduces non-uniformity in flow characteristics in the microfluidic device. Thus, it can be used for controlling practical microfluidic applications, such as mixing, mass, and heat transfer processes. This study has numerically investigated the charge-heterogeneity effects in the electroviscous (EV) flow of symmetric (1:1) electrolyte liquid through a uniform slit microfluidic device. The Poisson’s, Nernst-Planck (N-P), and Navier–Stokes (N-S) equations are numerically solved using the finite element method (FEM) to obtain the flow fields, such as total electrical potential (U), excess charge (n *), induced electric field strength (E x), and pressure (P) fields for following ranges of governing parameters: inverse Debye length (2 ≤ K ≤ 20), surface charge density (4 ≤ S 1 ≤ 16), and surface charge-heterogeneity ratio (0 ≤ S rh ≤ 2). Results have shown that the total potential (∣ΔU∣) and pressure (∣ΔP∣) drop maximally increase by 99.09% (from 0.1413 to 0.2812) (at K = 20, S 1 = 4) and 12.77% (from 5.4132 to 6.1045) (at K = 2, S 1 = 8), respectively with overall charge-heterogeneity (0 ≤ S rh ≤ 2). Electroviscous correction factor (Y, i.e., ratio of effective to physical viscosity) maximally enhances by 12.77% (from 1.2040 to 1.3577) (at K = 2, S 1 = 8), 40.98% (from 1.0026 to 1.4135) (at S 1 = 16, S rh = 1.50), and 41.35% (from 1 to 1.4135) (at K = 2, S rh = 1.50), with the variation of S rh (from 0 to 2), K (from 20 to 2), and S 1 (from 0 to 16), respectively. Further, a simple pseudo-analytical model is developed to estimate the pressure drop in EV flow, accounting for the influence of charge-heterogeneity based on the Poiseuille flow in a uniform channel. This model predicts the pressure drop ± 2%–4% within the numerical results. The robustness and simplicity of this model enable the present numerical results for engineering and design aspects of microfluidic applications.

Streaming electric field, electroviscous effect, and electrokinetic liquid flows in the induced pressure-driven transport of active liquids in narrow capillaries.

In this paper, we develop a theory for studying the electrokinetic effects in a charged nanocapillary filled with active liquid. The active particles present within the active liquid are self-driven, demonstrate vortex defects, and enforce a circumferentially arranged polarization field. Under such circumstances, there is the development of an induced pressure-gradient-driven transport dictated (similar to diffusioosmotic transport) by the presence of an axial gradient in the activity (or the concentration of the active particles). This pressure-driven transport has a profile different from the standard Hagen-Poiseuille flow in a nanocapillary. Also, this induced pressure-driven flow drives electrokinetic effects, which are characterized by the generation of a streaming electric field, associated electroosmotic (EOS) transport opposing pressure-driven flow, and electroviscous effect. We quantify these effects as functions of dimensionless parameters that vary inversely as the strength of the activity-induced pressure-driven flow and salt concentrations. Overall, we anticipate that this paper will draw immense attention toward a new type of activity-induced pressure-driven flow and associated electrokinetic phenomena in charged nanoconfinements.

Zeta Potentials of Cotton Membranes in Acetonitrile Solutions.

Solid surfaces in contact with nonaqueous solvents play a key role in electrochemistry, analytical chemistry, and industrial chemistry. In this work, the zeta potentials of cotton membranes in acetonitrile solutions were determined by streaming potential and bulk conductivity measurements. By applying the Gouy-Chapman theory and the Langmuir adsorption isotherm of ions to the experimental data, the mechanism of the electrification at the cotton/acetonitrile interface is revealed for the first time to be solely due to ion adsorption on the surface, rather than proton dissociation at the interface. Different salts were found to produce opposite signs of the zeta potentials. This behavior can be attributed to ion solvation effects and the strong ordering of acetonitrile molecules at the interface. Furthermore, a trend of the electroviscous effect was observed, in agreement with the standard electrokinetic theory. These findings demonstrate that electrokinetics in acetonitrile, a polar aprotic solvent, can be treated in the same manner as in water.

Influence of contraction ratio on electroviscous flow through the slit-type non-uniform microfluidic device

The electroviscous effects are relevant in controlling and manipulating the fluid, thermal, and mass transport microfluidic processes. The existing research has mainly focused on the fixed contraction ratio (dc, i.e., the area ratio of contraction to expansion) concerning the widely used contraction–expansion geometrical arrangement. This study has explored the influence of the contraction ratio (dc) on the electroviscous flow of electrolyte liquids through the charged non-uniform microfluidic device. The numerical solution of the mathematical model (Poisson's, Nernst–Planck, and Navier–Stokes equations) using a finite element method yields the local flow fields. In general, the contraction ratio significantly affects the hydrodynamic characteristics of microfluidic devices. The total electrical potential and pressure drop maximally change by 1785% (from −0.2118 to −3.9929) and 2300% (from −0.0450 to −1.0815), respectively, as the contraction ratio (dc) varies from 1 to 0.25. Furthermore, an electroviscous correction factor (Y, i.e., the ratio of apparent to physical viscosity) maximally enhances by 11.24% (at K = 8, S = 16 for 0.25≤dc≤1), 46.62% (at S = 16, dc=0.75 for 20≥K≥2), 22.89% (at K = 2, dc=0.5 for 4≤S≤16), and 46.99% (at K = 2, dc=0.75 for 0≤S≤16). Thus, the electroviscous effect is obtained maximum at dc=0.75 for the considered ranges of conditions. Finally, a pseudo-analytical model has been developed for a charged microfluidic device with variable contraction size (0.25≤dc≤1), based on the Hagen–Poiseuille flow in the uniform slit, which calculated the pressure drop within ±3% of the numerical results. The present numerical results may provide valuable guidelines for the performance optimization and design of reliable and essential microfluidic devices.

Streaming Potential and Associated Electrokinetic Effects through a Channel Filled with Electrolyte Solution Surrounded by a Layer of Immiscible and Dielectric Liquid.

The present article deals with the streaming potential-mediated pressure-driven flow across a channel in which the electrolyte solution is surrounded by a layer of cell membrane. Such a membrane of a biological cell may be modeled as an immiscible and dielectric liquid, which may bear free lipid molecules or charged surfactants. The presence of such additional charged molecules may lead to formation of liquid-liquid interfacial charge. In addition, the dielectric gradient-mediated ion partitioning effect further plays an important role in two-phase electrokinetic motion. We aim to study the generation of streaming potential and electrokinetic conversion efficiency as well as associated electroviscous effect for the undertaken problem. The mathematical model is based on the Poisson-Boltzmann equation for electrostatic potential and the Stokes equation for fluid flow, and the problem is studied considering suitable interfacial conditions for the flow variables along the liquid-liquid interface. The explicit analytical results for velocity and streaming field, electrokinetic energy conversion efficiency, and the parameter indicating the electroviscous effect are derived under the Donnan limit and within the Debye-Hückel electrostatic framework. We further numerically calculated the aforementioned intrinsic electrokinetic parameter associated with the problem undertaken for a wide range of pertinent parameters. The results are illustrated to indicate the impact of pertinent parameters on the generation of the streaming potential and associated electrokinetic effects.

Investigation into the Heat Transfer Behavior of Electrostatic Atomization Minimum Quantity Lubrication (EMQL) during Grinding

Electrostatic atomization minimum quantity lubrication (EMQL) technology has been developed to address the need for environmentally friendly, efficient, and low-damage grinding of challenging titanium alloy materials. EMQL leverages multiple physical fields to achieve precise atomization of micro-lubricants, enabling effective lubrication in high temperature, high pressure, and high-speed grinding environments through the use of electric traction. Notably, the applied electric field not only enhances atomization and lubrication capabilities of micro-lubricants but also significantly impacts heat transfer within the grinding zone. In order to explore the influence mechanism of external electric field on spatial heat transfer, this paper first comparatively analyzes the grinding heat under dry grinding, MQL, and EMQL conditions and explores the intensity of the effect of external electric field on the heat transfer behavior in the grinding zone. Furthermore, the COMSOL numerical calculation platform was used to establish an electric field-enhanced (EHD) heat transfer model, clarifying charged particles’ migration rules between poles. By considering the electroviscous effect, the study reveals the evolution of heat transfer structures in the presence of an electric field and its impact on heat transfer mechanisms.

Electroviscous effects in pressure-driven flow of electrolyte liquid through an asymmetrically charged non-uniform microfluidic device

BackgroundMicro-scale systems depict a different flow behavior from the macro-scale systems due to more vital surface forces such as surface tension, electrical charges, magnetic field, etc., which significantly affect the micro-scale flow. Further, among others, electrokinetic phenomena play a significant role at the micro-scale for controlling practical microfluidic applications. Therefore, it is essential to understand the fluid dynamics in micron-sized channels to develop efficient and reliable microfluidic devices. MethodsThe electroviscous effects in pressure-driven flow of electrolyte liquid through an asymmetrically charged contraction-expansion (4:1:4) slit microfluidic device have been investigated numerically. The mathematical model (i.e., Poisson's, Navier-Stokes, and Nernst-Planck equations) is solved using the finite element method to obtain the electrical potential, velocity, pressure, ion concentration fields, excess charge, an induced electric field strength for the following ranges of parameters: Reynolds number (Re=0.01), Schmidt number (Sc=1000), inverse Debye length (2≤K≤20), top wall surface charge density (4≤St≤16), surface charge density ratio (0≤Sr≤2) and contraction ratio (dc=0.25). Significant FindingsResults show that the charge asymmetry (Sr) at the different walls of the microfluidic device plays a significant role on the induced electric field development and microfluidic hydrodynamics. The total potential (|ΔU|) and pressure drop (|ΔP|) maximally increase by 197.45% and 25.46%, respectively with asymmetry of the charge. The electroviscous correction factor (ratio of apparent to physical viscosity) maximally changes by 20.85% (at K=2, St=16 for 0≤Sr≤2), 34.16% (at St=16, Sr=2 for 2≤K≤20), and 39.13% (at K=2, Sr=2 for 0≤St≤16). Thus, charge asymmetry (0≤Sr≤2) remarkably influences the fluid flow in the microfluidic devices, which is used for controlling the microfluidic processes, such as, mixing efficiency, heat, and mass transfer rates. Further, a simpler analytical model is developed to predict the pressure drop in electroviscous flow considering asymmetrically charged surface, based on the Poiseuille flow in the individual uniform sections and pressure losses due to orifice, estimates the pressure drop 1–2% within the numerical results. The robustness of this model enables the use of present numerical results for design aspects in the microfluidic applications.

Giant Electroviscous Effects in a Ferroelectric Nematic Liquid Crystal

The electroviscous effect deals with the change in the viscosity of fluids due to an external electric field. Here, we report experimental studies on the electroviscous effects in a ferroelectric nematic liquid crystal. It is synthesized by accomplishing an optimized synthetic route, which provides higher yield than the conventional one. We measure electric-field-dependent viscosity under a steady shear at different temperatures. In the low-field range, the increase in viscosity [$\mathrm{\ensuremath{\Delta}}\ensuremath{\eta}=\ensuremath{\eta}(E)\ensuremath{-}{\ensuremath{\eta}}_{0}$] is proportional to ${E}^{2}$ and the corresponding viscoelectric coefficient [$f\ensuremath{\approx}{10}^{\ensuremath{-}9}\phantom{\rule{0.2em}{0ex}}{\mathrm{m}}^{2}/{\mathrm{V}}^{2}$] of the ferroelectric nematic is 2 orders of magnitude larger than the apolar nematic liquid crystals and the largest ever measured for a fluid. The apparent viscosity measured under a high electric field shows a power-law divergence $\ensuremath{\eta}\ensuremath{\sim}(T\ensuremath{-}{T}_{c}{)}^{\ensuremath{-}0.7\ifmmode\pm\else\textpm\fi{}0.05}$, followed by nearly an order of magnitude drop below the $N$-${N}_{F}$ phase transition. Experimental results within the dynamical scaling approximation demonstrate rapid growth of polar domains under a strong electric field as the $N$-${N}_{F}$ phase transition is approached. The gigantic electroviscous effects demonstrated here are useful for emerging applications and understanding striking electrohydromechanical effects in ferroelectric nematic liquid crystals.

Mathematical and computational modeling of electrohydrodynamics through a nanochannel

Fluid-ion transport through a nanochannel is studied to understand the role and impact of different physical phenomena and medium properties on the flow. Mathematically, the system is described through coupled fourth order Poisson–Nernst–Planck–Bikerman and Navier–Stokes equations. The fourth order-Poisson–Nernst–Planck–Bikerman model accounts for ionic and nonionic interactions between particles, the effect of finite size of the particles, polarization of the medium, solvation of the ions, etc. Navier–Stokes equations are modified accordingly to include both electroviscous and viscoelectric effects and the velocity slip. The governing equations are discretized using the lattice Boltzmann method. The mathematical model is validated by comparing the analytical and experimental ion activity while the numerical model is validated by comparing the analytical and numerical velocity profiles for electro-osmotic flow through a microchannel. For a pressure driven flow, the electroviscous and viscoelectric effects decrease the fluid velocity while the velocity slip enhances it. The acidity of the medium also influences the fluid velocity by altering the ζ potential and ion concentration. The finite size of the particle limits the concentration of ionic species, thus, reducing electroviscous effects. As the external concentration decreases, the impact of finite size of particles also reduces. The inhomogeneous diffusion coefficient also influences electroviscous effects as it changes the concentration distribution. The variation in external pressure does not influence the impact of steric and viscoelectric effects significantly. The maximum impact is observed for ΔP = 0 (electro-osmotic flow).

Investigation on gas/water two-phase flow in quartz nanopores from molecular perspectives

Understanding the gas/water two-phase occurrence, flow patterns, and underlying mechanisms in quartz nanopores is crucial for gas transport and production in shale reservoirs. In this study, we investigated the flow characteristics of methane and water in hydroxylated quartz nanopores employing the grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations and focused on elucidating the effects of water saturation, pressure gradient and ion concentration in various aperture nanopores. Results show that water molecules preferentially adsorb on the hydrophilic quartz surface to form water film, increasing methane flow friction and reducing its slippage velocity significantly. Water bridges are formed to wrap gas bubbles and hinder the gas flow with increased water saturation. The water phase occupies a larger pore space with increasing water saturation resulting in an increase in methane effective viscosity and a decrease in apparent permeability. The water bridge is broken under the joint action of external force and gas driving when the pressure gradient is much larger, leading to a dramatic growth of gas flow, and the high-speed gas will produce a shear driving effect on the thick water layers. Ions will weaken the formation of hydrogen bonds between water molecules, but the flux of the water phase decreases with the increasing ion concentration due to the combined impact of ion spatial structure and electroviscous effects and counteracts the gas phase, thus impeding its flow. This study shed light on the flow phenomena of gas/water phases in hydrophilic nanopores. The results are expected to provide some insight into energy and environmental issues, such as fracturing fluid optimization, enhanced gas recovery (EGR) by water flooding, and the fabrication of microfluidic chips.

Electro-viscous effect of nanofluid flow over a rotating disk

In this research work, we investigate an unsteady flow over a rotating disk. We assign symbols to the selected dependent and independent quantities. Then all physical systems are modeled to mathematical form by applying physical laws for an ionized liquid flow over a rotating disk with nanoparticles from the set of Poisson Nernst–Planck model, Energy equation and Navier–Stokes equations. The set of partial differential equations along with the boundary conditions are transformed to a set of coupled ordinary differential equations for an electro-viscous flow of nanofluid over a rotating disk by using similarity transformations. The unknown physical quantities are investigated through Parametric Continuation Method (PCM). For physical purpose, physical quantities like flow behavior thermal properties, thermal variation, the distribution of ions in the fluid region, skin friction, are analyzed through graphical and tabulated results. As exact solutions are not possible for nonlinear ordinary differential equations (ODEs) system, therefore, such quantities are subjected to numerical calculation following Parametric Continuation Method (PCM) and validated the result through BVP4c package in Matlab.

Analysis of electroviscous effect and heat transfer for flow of non-Newtonian fluids in a microchannel with surface charge-dependent slip at high zeta potentials

In hydrophobic surfaces, pressure-driven flows induce electrokinetic flow retardation, where the slip length decreases due to the surface charge. In the current work, we investigate the thermal transport and fluid flow behavior of a pressure-driven flow of shear-thinning fluid with an electroviscous effect, accounting for the influence of surface charge on the slip. The electrical potential field induced in the electrical double layer (EDL), velocity, streaming potential, and temperature is obtained after solving the Poisson–Boltzmann equation, mass, momentum, and energy conservation equations without invoking the Debye–Hückel linearization. Results are presented for a broad range of dimensionless parameters, such as surface charge-independent slip length, Debye–Hückel parameter, zeta potential, heat flux, and flow consistency index (n). The flow velocity decreases after considering the effect of surface charge on slip, and such decrement is more for lower value of n, higher magnitude of zeta potential, and thicker EDL. Moreover, for lower value of n (1/3), the alteration of the Nusselt number with the surface charge is non-monotonic, whereas it increases with the surface charge magnitude for higher value of n (1/2). Further, for lower value of n, the Nusselt number enhances by the surface charge effect on the slip, whereas, for higher value of n, the trend is the opposite. Also, there is a strong interplay of the rheology of the fluid and EDL thickness in dictating the variation of the Nusselt number.

The coupling effects of pore structure and rock mineralogy on the pre-Darcy behaviors in tight sandstone and shale

The pore structure and mineral composition play a crucial role in controlling the water flow behaviors of low-permeability media, which is characterized by threshold pressure gradient (TPG) and nonlinear flow curve. To figure out the coupling effects of these two factors on pre-Darcy flow regimes, water flow experiments were conducted on four tight sandstones, three shales and one fractured shale. The results indicate that both the TPG and pseudo threshold pressure gradient (PTPG) decrease with an increase in total porosity and macropores porosity. The variation of the nonlinear exponent (n) with total porosity and macropore porosity can be described by an exponential function with three parameters. The clay minerals and brittle minerals exert completely opposite influence on the variation of pre-Darcy flow parameters (PTPG, TPG and n). Both TPG/PTPG and n increase with increasing clay content while reduce with increase in the brittle minerals content. Theoretical analyses based on the disjoining pressure demonstrate that immovable water and electro-viscous effect are mainly responsible for water flow deviating from Darcy's law in tight sandstone and shale. Calculation results show that the proportion of immovable water of intact samples ranges from 23.46% to 89.73%, the movable water content ranges from 10.27%–76.54%. The pre-Darcy flow parameters exponentially increase with increase in immovable water content while exponentially decrease with increasing proportion of movable water. For the shale sample used in this work, the immovable water and electro-viscous effect contributing to the pre-Darcy flow account for 81.11%–90.35% and 9.58%–18.51%, respectively. The different flow regimes are controlled by the pore diameter and the thickness of water with shear fluidity. If the diameter of interconnected pores is larger than 10 μm, the Darcy flow regime dominates. When the diameter of minor pore throat of the flow channels are less than 33.82 nm for sandstones and 37.68 nm for shales, the movement of water in this flow channel would generate the TPG.

Stimuli-responsive polyelectrolyte brushes for regulating streaming current magnetic field and energy conversion efficiency in soft nanopores

The electrokinetic energy conversion, electroviscous effect, and induced internal and external magnetic fields in a smart polyelectrolyte grafted “soft” nanopore with pH responsiveness are studied here using an efficient molecular theory approach. The analysis is based on writing the total free energy of the system, including the conformational entropy of the flexible, self-avoiding polymer chains and the translational entropy of the mobile species, the electrostatic interactions, and the free energy due to chemical equilibrium reactions. Then, the free energy is minimized, while satisfying the necessary constraints to find the equilibrium state of the system. The predictions of the model are shown to be in excellent agreement with analytical solutions derived for special cases. We discuss the effect of different influential environmental and polymer brush parameters in detail and show that the electrokinetic energy conversion efficiency is optimal at moderate pH values and low background salt concentrations. It is also shown that the electrokinetic energy conversion efficiency is a complex function depending on both the environmental and polymer brush properties. Notably, high slip coefficients or high polymer grafting densities do not necessarily lead to a high energy conversion efficiency. Magnetic field readouts allow to measure streaming currents through nanopores without the need of electrodes and may be utilized as a secondary electronic signature in nanopore sensing techniques. It is shown that in nanopores modified with polyelectrolyte brushes, the induced magnetic fields can be tens of times larger than those in solid-state nanopores having only surface charges. We show that by tuning the pH, background salt concentration, surface charge, and polyelectrolyte grafting density, the magnitude of the internal and external magnetic fields can be significantly changed and controlled in a wide range.

Electroviscous effects in charge-dependent slip flow of liquid electrolytes through a charged microfluidic device

This work investigates electroviscous effects in the presence of charge-dependent slip in steady pressure-driven laminar flow of a symmetric (1:1) electrolyte liquid through a uniformly charged slit contraction–expansion (4:1:4) microfluidic device. The mathematical model comprising the Poisson’s, the Nernst–Planck, the Navier–Stokes, and the current continuity equations are solved numerically using the finite element method (FEM). The flow fields (electrical potential, charge, induced electric field strength, pressure drop, and electroviscous correction factor) have been obtained and presented for the wide range of the governing parameters like inverse Debye length (2≤K≤20), surface charge density (4≤S≤16) and the slip length (0≤B0≤0.20) at fixed Schmidt number (Sc=1000) and low Reynolds number (Re=0.01). The flow fields have shown complex dependence on the governing parameters. The charge-dependent slip has further enhanced the complexity of the dependency in comparison to the no-slip condition. In presence of charge-dependent slip, the total electrical potential (|ΔU|) maximally increases by 78.68% and pressure drop (|ΔP|) maximally decreases by 63.42%, relative to no-slip flow, over the ranges of conditions. The electroviscous correction factor (Y= ratio of apparent to physical viscosity) increases by 33.58% under the no-slip (B0=0) condition. In contrast, the electroviscous correction factor (Y) increases maximally by 72.10% for charge-dependent slip than that in the no-slip flow for the considered ranges of the conditions. A simple analytical model to estimate the pressure drop in the electroviscous flow has been developed based on the Poiseuille flow in the individual uniform sections and pressure loss due to thin orifice. The model overpredicts the pressure drop by 2%–4% from the numerical values. Finally, the predictive relations, depicting the functional dependence of the numerical results on the governing parameters, are presented for their practical use in the design and engineering of microfluidic devices.

The electroviscous effect in nanochannels with overlapping electric double layers considering the height size effect on surface charge

The electroviscous effect has been extensively investigated in micro/nano scale ions transport, fluidic flow and heat transfer, etc. Previous researches often used constant surface charge in theoretic calculation and numerical simulations. However, for thick overlapping electric double layer (EDL) nanochannels, the channel height size effect on surface charge cannot be neglected. In this work, we consider the channel height size effect on surface charge to investigate the related ions transport, fluidic flow and heat transfer in nanochannels. The corresponding results show that the deviation considering the height effect or not is significant, especially in the situation of boundary slip. The relative errors of local ionic concentration and potential can reach 50% and 8%, respectively. The maximum relative errors of induced electrical field strength and the ratio of apparent viscosity to fluidic viscosity reach 10% and 9%, respectively, indicating strong height size effect on the fluidic flow. The deviation of Nu is relatively small and almost not affected by the surface charge. These deviations will decrease to zero when the channel height is large enough or the solution concentration is high enough to reach a non-overlapping EDL situation. The results of this work are meaningful to further understand the electroviscous effect in nanochannels, which may provide useful guidelines for the design and performance optimization of nanofluidic devices.

A study for the longitudinal permeability of fibrous porous media with consideration of electroviscous effects

We investigate theoretically the longitudinal permeability for the electroviscous flow through one-dimensional (1D) fibrous porous media with orderly and disorderly fiber arrays. The structures of fibrous porous media are idealized as circular unit cells. In the cell, the dimensionless net charge density is given by solving the linearized Poisson-Boltzmann equation, and is approximated as 1 by detailed discussions. Based on the approximate value of the net charge density, circular unit cell and Voronoi Tessellation method, we propose mathematical models for the longitudinal permeability with considering electroviscous effects. The effects of the fiber volume fraction, fiber radius and electroviscous resistance number on the longitudinal permeability are analyzed in detail. Moreover, there are good agreements between the present predictions and these results from the literatures.

Electroviscous Effect of Water-Base Nanofluid Flow between Two Parallel Disks with Suction/Injection Effect

This article, investigates the behaviour of an ionized nanoliquid motion regarding heat transmission between two parallel discs. In the proposed model, the squeezing flow of Cu-water nanofluid with electrical potential force is analysed for studying the flow properties and an uniform magnetic field is applied to that fluid, by taking the surface of the bottom disc porous. We have also studied the effects of different nanomaterials on the transmission of heat through nanofluids. Furthermore, the influence of various physical parameters in the proposed model of nanofluids flow like volume fraction of nanomaterials, squeezing number, Hartmann number, Eckert number, and Prandtl number are analysed and discussed quantitatively through various tables and graphs. The system of nonlinear partial differential equations (PDE’s) has been used to formulate the proposed flow model and later converted to a set of nonlinear ODE’s by mean similarity transformation. Further, the reduced form of ODEs has been solved by Parametric Continuation Method (PCM), which is a stable numerical scheme. The outcomes obtained from the proposed model could also be used to analyse nanofluid flow in several fields, such as polymer processing, power transfer and hydraulic lifts.

Electroosmotic modulated unsteady squeezing flow with temperature-dependent thermal conductivity, electric and magnetic field effects

Modern lubrication systems are increasingly deploying smart (functional) materials. These respond to various external stimuli including electrical and magnetic fields, acoustics, light etc. Motivated by such developments, in the present article unsteady electro-magnetohydrodynamics squeezing flow and heat transfer in a smart ionic viscous fluid intercalated between parallel plates with zeta potential effects is examined. The proposed mathematical model of problem is formulated as a system of partial differential equations (continuity, momenta and energy). Viscous dissipation and variable thermal conductivity effects are included. Axial electrical distribution is also addressed. The governing equations are converted into ordinary differential equations via similarity transformations and then solved numerically with MATLAB software. The transport phenomena are scrutinized for both when the plates move apart or when they approach each other. Also, the impact of different parameters such squeezing number, variable thermal conductivity parameter, Prandtl number, Hartmann number, Eckert number, zeta potential parameter, electric field parameter and electroosmosis parameter on the axial velocity and fluid temperature are analysed. For varied intensities of applied plate motion, the electro-viscous effects derived from electric double-capacity flow field distortions are thoroughly studied. It has been shown that the results from the current model differ significantly from those achieved by using a standard Poisson–Boltzmann equation model. Axial velocity acceleration is induced with negative squeeze number (plates approaching, S < 0) in comparison to that of positive squeeze number (plates separating, S > 0). Velocity enhances with increasing electroosmosis parameter and zeta potential parameter. With rising values of zeta potential and electroosmosis parameter, there is a decrease in temperatures for U e > 0 for both approaching i.e. squeezing plates (S < 0) and separating (S > 0) cases. The simulations provide novel insights into smart squeezing lubrication with thermal effects and also a solid benchmark for further computational fluid dynamics investigations.