Electroosmotic Flow Of Power-law Fluids Research Articles

Rotational electroosmotic slip flow of power-law fluid at high zeta potential in variable-section microchannel

In this paper we study the rotating electroosmotic flow of a power-law fluid with Navier slip boundary conditions under high zeta potential subjected to the action of a vertical magnetic field in a variable cross-section microchannel. Without using the Debye–Hückel linear approximation, the finite difference method is used to numerically calculate the potential distribution and velocity distribution of the rotating electroosmotic flow subjected to an external magnetic field. When the behavior index <inline-formula><tex-math id="M4">\begin{document}$n = 1$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M4.png"/></alternatives></inline-formula>, the fluid obtained is a Newtonian fluid. The analysis results in this paper are compared with the analytical approximate solutions obtained in the Debye–Hückel linear approximation to prove the feasibility of the numerical method in this paper. In addition, the influence of behavior index <i>n</i>, Hartmann number <i>Ha</i>, rotation angular velocity <inline-formula><tex-math id="M5">\begin{document}$\Omega $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M5.png"/></alternatives></inline-formula>, electric width <i>K</i> and slip parameters <inline-formula><tex-math id="M6">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20212327_M6.png"/></alternatives></inline-formula> on the velocity distribution are discussed in detail. It is obtained that when the Hartmann number <i>Ha</i> > 1, the velocity decreases with the increase of the Hartmann number <i>Ha</i>; but when the Hartmann number <i>Ha</i> < 1, the magnitude of the <i>x</i>-direction velocity <i>u</i> increases with the augment of <i>Ha</i>.

Steric and Slippage Effects on Mass Transport by Using an Oscillatory Electroosmotic Flow of Power-Law Fluids.

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement.

Mass transport by an oscillatory electroosmotic flow of power-law fluids in hydrophobic slit microchannels

In this work, we study the hydrodynamics, concentration field, and mass transport of species due to an oscillatory electroosmotic flow that obeys a power law. An additional aspect that is considered in the analysis corresponds to the effect of the slippage condition at the walls of the microchannel. The governing equations that describe the involved phenomena are the following: equation of Poisson–Boltzmann for the electrical potential in the electric double layer, the momentum equation, and the species transport equation. These equations were simplified with the aid of the lubrication theory and were numerically solved by using a conventional finite difference scheme. Our results suggest that, under the slippage effects, the best conditions can be promoted for the mass transport of species for different values of the Schmidt number and Womersley numbers less than unity, and even it is maximized up to two orders of magnitude when $${\text {Wo}}>1$$ . In the analysis, the cross-over phenomenon appears for the mass transport for different species and it is identified for both Newtonian and non-Newtonian fluids. For shear-thinning fluids with slippage at the microchannel walls, the cross-over phenomenon occurs, and the species with less diffusivity can be transported up to ten times faster in comparison with Newtonian fluids when the no-slip effect is considered.

Numerical Analysis and Entropy Generation of Electrokinetic Flow of Power-Law Fluid in a Microtriangular Prism

This research aims to study the characteristics of thermal transport and analyse the entropy generation of electroosmotic flow of power-law fluids in a microtriangular prism in the presence of pressure gradient. Considering a fully developed flow subject to constant wall heat flux, the nonlinear electric potential, momentum, and linear heat transfer equations are solved numerically by developing an iterative finite difference method with a nonuniform grid. The thermal efficiency of the model is explored under the light of the second law of thermodynamics. Effect/impact of governing physical parameters on velocity, temperature, Nusselt number, and entropy distributions is studied, and the results are demonstrated graphically; we found that the Nusselt number decreases with the increase of power-law index, and average entropy generation increases with power-law index. We believe that the obtained result in the present study shall be useful for design of energy efficient microsystems which utilize the dual electrokinetic and centrifugal pumping effects.

Enhanced Electro-Osmotic Flow of Power-Law Fluids in Hydrophilic Patterned Nanochannel

Abstract In this paper, electro-osmotic flow (EOF) enhancement of non-Newtonian power-law fluids in a modulated nanochannel with polarized wall is proposed. The channel walls are embedded with periodically arranged rectangular grooves, placed vertically with the direction of electric field. The key aspect of the present study is to achieve enhanced EOF of power-law fluids due to periodic groove patterns. The flow characteristics are studied through Poisson–Nernst–Plank-based Navier–Stokes model associated with electrochemical boundary conditions. Some random-phase differences between the grooves in both the walls are allowed to find the best configuration for the EOF enhancement in case of both Pseudo-plastic fluid, Dilatant fluid, and compared to Newtonian fluid. A notable enhancement factor is observed when groove width is much larger than its depth along with overlapped EDL. It is also found that EOF enhancement for shear-thinning fluid is quite better than the other fluids, for the same set of physical parameters. A comparison of enhancement factor for power-law fluid is also presented when the grooves are replaced with hydrophobic strips. It is worth to mention here that the present study assumes no-slip condition which is true for wetting (hydrophilic) surface over nonwetting (hydrophobic) strips which is common occurrence in regards to nanoconfinements.

Rotating electroosmotic flow of power-law fluid through polyelectrolyte grafted microchannel

Due to evergrowing importance of understanding flow of bio-fluids in Lab-on-CD based systems, we investigate the flow behaviour of power-law fluids in the rotating electroosmotic flow through a polyelectrolyte grafted (soft) narrow channel. We use an in-house numerical code to solve the governing transport equations for the velocities and flow rates in a rotating channel subjected to an applied external electric field. We show the strong effect of polyelectrolyte layer on the flow behaviour and find an increase in flow rate as we increase the size of the polyelectrolyte layer. We also show that rheology strongly influences the interplay of the Coriolis forces due to rotation and electrical body force due to the applied electric field. We show that the velocities are generally higher for shear thinning fluids as compared to shear thickening fluids. We also show that presence of polymer brushes in the polyelectrolyte layer creates a drag on the fluid which reduces velocities. We also show that the flow rates are strongly altered by the effect of rotation and that shear thickening fluids have lower flow rates than shear thinning fluids. The effect of fluid rheology on the shear stress distribution is also discussed. We believe that studying effect of fluid rheology becomes very important for designing soft channel based Lab-on-CD systems driven by electroosmotic forcing and dealing with rheologically complex bio-fluids such as blood, saliva or mucus.

An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces.

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell’s first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.

Electroosmotic flow of power-law fluids in curved rectangular microchannel with high zeta potentials

In this article, electroosmotic flow of non-Newtonian fluids through a curved rectangular microchannel is studied numerically. The power-law model is used to simulate the rheological behavior of fluid. Moreover, the flow is assumed to be hydrodynamically fully developed and the walls carry high zeta potentials. To do so, the Poisson–Boltzmann equation without imposing the Debye–Hückel linear approximation is solved by applying the central difference scheme. Furthermore, the continuity and Cauchy momentum equations in the cylindrical coordinate system are solved using SIMPLE finite-volume method. Consequently, the effects of governing parameters such as flow behavior index, electrokinetic separation distance, curvature, zeta potential, and channel aspect ratio on the flow field and hydrodynamic characteristics are studied in details. The results show that the secondary flows which are created in shear-thinning fluid flows are stronger in comparison to that of shear-thickening and Newtonian fluid flows. Also, the variation of electrokinetic separation distance changes the secondary flow patterns in shear-thinning fluid flows, and it does not have a monotonic effect on the strength of secondary flows. Moreover, the obtained results for shear-thinning and Newtonian fluid flows indicate that the increasing of curvature, in addition to increasing the circulation strength considerably, also causes the volumetric flow rate to slightly increase. Furthermore, it is found that the increasing of zeta potential can be employed in shear-thinning fluid flows in order to significantly increase the volumetric flow rate and the performance of mixing. Additionally, it is observed that the increasing of channel aspect ratio leads to an increase in the circulation strength of shear-thinning fluid flow.

Approximate Solution for Electroosmotic Flow of Power-Law Fluids in a Planar Microchannel with Asymmetric Electrochemical Boundary Conditions.

Electroosmotic flow (EOF) is widely used in microfluidic systems and chemical analysis. It is driven by an electric force inside microchannel with highly charged boundary conditions. In practical applications, electrochemical boundary conditions are often inhomogeneous because different materials as walls are commonly utilized in routine fabrication methods. In the present study, we focus on the analytic solutions of the EOF generated in a planar microchannel with asymmetric electrochemical boundary conditions for non-Newtonian fluids. The velocity profile and flow rate are approximated by employing the power-law model of fluids in the Cauchy momentum equation. The hydrodynamic features of the EOF under asymmetric zeta potentials are scrutinized as a function of the fluid behavior index of the power-law fluid, thickness of Debye length, and zeta potential ratios between planes. The approximate solutions of the power-law model are comparable to the numerically obtained solutions when the Debye length is small and the fluid behavior index is close to unity. This study provides insights into the electrical control of non-Newtonian fluids, such as biological materials of blood, saliva, and DNA solution, in lab-on-a-chip devices.

Particle manipulation via integration of electroosmotic flow of power-law fluids with standing surface acoustic waves (SSAW)

Standing surface acoustic wave (SSAW) based microfluidic devices have shown great promise toward fluid and particle manipulation applications in medicine, chemistry, and biotechnology. In this article, we present an analytical model for investigating continuous manipulation of particles (both synthetic and biological) within electroosmotic flow of non-Newtonian bio-fluids in a microfluidic channel under the influence of standing surface acoustic waves (SSAW). The particles are injected along the center of channel into the electroosmotically driven flow of power-law fluids, wherein their transport through the SSAW region is dictated by the hydrodynamic, electrophoretic, and acoustic forces. We first present a mathematical model to analyze the characteristics of electroosmotic flow of non-Newtonian power-law fluids in a hydrophobic slit microchannel. Next, we investigate the trajectories of particles in the flow field due to the combined effect of electroosmotic, electrophoretic, and acoustophoretic forcing mechanisms. The effect of key parameters such as particle size, their physical properties, input power, flow rate, and flow behavior index on the particle trajectories is examined while including the effect of the channel walls. The presented model delineates the methodologies of improving SSAW-based particle separation technology by considering the fluid rheology as well as the surface properties of the channel walls. Therefore, we believe that this model can serve as an efficient tool for device design and quick optimizations to explore novel applications concerning the integration of electroosmotic flows with acoustofluidic technologies.

The Parametric Study of Electroosmotically Driven Flow of Power-Law Fluid in a Cylindrical Microcapillary at High Zeta Potential.

Due to the increasingly wide application of electroosmotic flow in micromachines, this paper investigates the electroosmotic flow of the power-law fluid under high zeta potential in a cylindrical microcapillary for different dimensionless parameters. The electric potential distribution inside a cylindrical microcapillary is presented by the complete Poisson-Boltzmann equation applicable to an arbitrary zeta potential. By solving the Cauchy momentum equation of power-law fluids, the velocity profile, the volumetric flow rate, the average velocity, the shear stress distribution and dynamic viscosity of electroosmotic flow of power-law fluids in a cylindrical microcapillary are studied for different low/high zeta potential, flow behavior index, dimensionless electrokinetic width. The velocity profile gradually changes from parabolic to plug-like shape as the flow behavior index decreases or as the dimensionless electrokinetic width increases. For shear thinning fluids, the viscosity is greater in the center of the microchannel than that near the channel wall, the reverse is true for the shear thickening fluids. Greater volumetric rate and average velocity can be achieved by enhancing the dimensionless electrokinetic width, flow behavior index and zeta potential. It is noted that zeta potential and flow behavior index are important parameters to adjust electroosmotic flow behavior in a cylindrical microcapillary.

Electroosmotic Flows of Power-Law Fluids with Asymmetric Electrochemical Boundary Conditions in a Rectangular Microchannel

In this paper, a systematic study of a fully developed electroosmotic flow of power-law fluids in a rectangular microchannel bounded by walls with different zeta potentials is described. Because the upper and lower layers of most microchannels are made of different materials, it is necessary to study the flow characteristics for cases in which the microchannels have different zeta potentials at each wall. The electrical potential and momentum equations were solved numerically using a finite element analysis. The velocity profiles and flow rates were studied parametrically by varying the fluid behavior index, channel aspect ratio, and electrochemical properties of the liquid and the bounding walls. The calculated volumetric flow rates in a rectangular microchannel were compared with those between two infinite parallel plates.

Dynamic Electroosmotic Flows of Power-Law Fluids in Rectangular Microchannels

Dynamic characteristics of electroosmosis of a typical non-Newtonian liquid in a rectangular microchannel are investigated by using numerical simulations. The non-Newtonian behavior of liquids is assumed to obey the famous power-law model and then the mathematical model is solved numerically by using the finite element method. The results indicate that the non-Newtonian effect produces some noticeable dynamic responses in electroosmotic flow. Under a direct current (DC) driving electric field, it is found that the fluid responds more inertly to an external electric field and the steady-state velocity profile becomes more plug-like as the flow behavior index decreases. Under an alternating current (AC) driving electric field, the fluid is observed to experience more significant acceleration and the amplitude of oscillating velocity becomes larger as the fluid behavior index decreases. Furthermore, our investigation also shows that electroosmotic flow of power-law fluids under an AC/DC combined driving field is enhanced as compared with that under a pure DC electric field. These dynamic predictions are of practical use for the design of electroosmotically-driven microfluidic devices that analyze and process non-Newtonian fluids such as biofluids and polymeric solutions.

Electro-osmotic flow of power-law fluid and heat transfer in a micro-channel with effects of Joule heating and thermal radiation

A mathematical model has been developed for studying the electro-osmotic flow and heat transfer of bio-fluids in a micro-channel in the presence of Joule heating effects. The flow of bio-fluid is governed by the non-Newtonian power-law fluid model. The effects of thermal radiation and velocity slip condition have been examined in the case of hydrophobic channel. The Poisson–Boltzmann equation governing the electrical double layer field and a body force generated by the applied electric potential field are taken into consideration. The results presented here pertain to the case where the height of the channel is much greater than the thickness of electrical double layer comprising the Stern and diffuse layers. The expressions for flow characteristics such as velocity, temperature, shear stress and Nusselt number have been derived analytically under the purview of the present model. The results estimated on the basis of the data available in the existing scientific literatures are presented graphically. The effects of thermal radiation have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding the heat transfer in micro-channel in the presence of electric potential. The dimensionless Joule heating parameter has a reducing impact on Nusselt number for both pseudo-plastic and dilatant fluids, nevertheless its impact on Nusselt number is more pronounced for dilatant fluid. Furthermore, the effect of viscous dissipation has a significant role in controlling heat transfer and should not be neglected.

Electroosmotic flow of a power-law fluid through an asymmetrical slit microchannel with gradually varying wall shape and wall potential

• Non-parallel electroosmotic flow of power-law fluid in a microchannel. • Lubrication theory for slowly varying channel height and wall potential. • Linear superposition of forces invalidated by asymmetry of channel. • Nonlinear interaction between wall undulation and wall charge modulation. • Flow-rate sensitive to phase shift of wall patterns and power-law index. This study aims to investigate electroosmotic flow of a power-law fluid through a slit channel with walls asymmetrically patterned with periodic variations in shape and zeta potential. On taking into account the near-wall depletion layer, the present problem is simplified on the basis of the lubrication approximation, and through the use of the Helmholtz–Smoluchowski slip boundary condition. Nonlinear equations are to be solved for two unknown functions of axial dependence, one being the induced pressure gradient, and another being an undetermined stress component. An efficient numerical scheme is devised in this work to solve the nonlinear problem. Results are generated to check whether the principle of linear superposition of forces, for electrokinetic flow of a non-Newtonian fluid in the presence of a Newtonian depletion layer, is still applicable to flow in an asymmetric channel. It is also found that phase shifts between the geometrical and electric potential patterns on the two walls may lead to qualitatively disparate effects, depending on the power-law behavior index of the fluid and the applied pressure gradient.

Pressure effects on electroosmotic flow of power-law fluids in rectangular microchannels

In this paper, the fully developed electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A complete parametric study reveals that the pressure effects are more pronounced at higher values of the channel aspect ratio and smaller values of the flow behavior index. The Poiseuille number is found to be an increasing function of the channel aspect ratio for pressure assisted flow and a decreasing function of this parameter for pressure opposed flow. It is also observed that the Poiseuille number is increased by increasing the zeta potential. Furthermore, the results show that an increase in the flow behavior index results in a lower flow rate ratio, defined to be the ratio of the flow rate to that of a Newtonian fluid at the same conditions. Moreover, whereas the flow rate ratio in the presence of an opposed pressure gradient is smaller than that of a favorable pressure force for shear thinnings, the opposite is true for shear-thickening fluids.

Thermal transport characteristics pertinent to electrokinetic flow of power-law fluids in rectangular microchannels

In the present study, the thermal characteristics of electroosmotic flow of power-law fluids in rectangular microchannels in the presence of pressure gradient are investigated. The governing equations for fully developed flow under H1 thermal boundary conditions are first made dimensionless and subsequently solved through a finite difference procedure for a non-uniform grid. The influence of the major parameters on thermal features of the flow such as the temperature distribution and Nusselt number is discussed by a complete parametric study. The results reveal that the channel aspect ratio and the non-Newtonian characteristic of the fluid can affect the thermal behavior of the flow. It is observed that decreasing the channel aspect ratio causes the energy generated due to the viscous heating to become more significant. Furthermore, the viscous dissipation is higher for shear-thickening fluids. The Nusselt number is ascertained to be an increasing function of the channel aspect ratio regardless of the flow behavior index and pressure gradient. Moreover, the results suggest that increasing the flow behavior index can either increase or decrease the Nusselt number, depending on the thermal conditions of the flow.

Thermally Fully Developed Electroosmotic Flow of Power-Law Fluids in a Circular Microchannel

ABSTRACTThis study presents a thermally fully developed electroosmotic flow of the non-Newtonian power-law fluids through a circle microchannel. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including the Poisson Boltzmann equation, the modified Navier Stokes equation and the energy equation is developed. The semi-analytical solutions of normalized velocity and temperature are derived. The velocity profile is computed by numerical integrate, and the temperature distribution is obtained by finite difference method. Results show that the velocity profiles depend greatly on the fluid behavior index n and the nondimensional electrokinetic width K. For a specified value of K, the axial velocity increases with a decrease in n, and the same trend for the effect of K on the velocity can be found for a specified value of n. Moreover, the dimensionless temperature is governed by three parameters, namely, the flow behavior index n, the nondimensional electrokinetic width K, and the dimen-sionless Joule heating parameter G. The variations of radial fluid temperature distributions with different parameters are investigated.

Electrokinetically driven fluidic transport of power-law fluids in rectangular microchannels

Electroosmosis is the predominant mechanism for flow generation in lab-on-chip devices. Since most biofluids encountered in these devices are considered to be non-Newtonian, it is vital to study the flow characteristics of common non-Newtonian models under electroosmotic body force. In this paper, the hydrodynamically fully developed electroosmotic flow of power-law fluids in rectangular microchannels is analyzed. The electrical potential and momentum equations are numerically solved through a finite difference procedure for a non-uniform grid. A thoroughgoing parametric study reveals that the Poiseuille number is an increasing function of the channel aspect ratio, the zeta potential, the flow behavior index, and the dimensionless Debye–Hückel parameter. It is also found that the validity range of the Debye–Hückel approximation for shear-thickening fluids is much wider than that of shear-thinnings. Furthermore, while the dimensionless mean velocity is an increasing function of the channel aspect ratio and the dimensionless Debye–Hückel parameter, it is a decreasing function of the flow behavior index. Moreover, to increase the zeta potential is to increase the dimensionless mean velocity for shear-thinnings, nevertheless, its effect is not significant for shear-thickenings.

Thermally developing electroosmotic flow of power-law fluids in a parallel plate microchannel

The present investigation considers the thermally developing electroosmotic flow of power-law fluids through a parallel plate microchannel. Both the viscous dissipation and Joule heating effects are taken into account and a step change in wall temperature is considered to represent physically conceivable thermal entrance conditions. Expressions for the dimensionless temperature and Nusselt number in the form of infinite series are presented. In general, the resultant eigenvalue problem is solved numerically; nevertheless, an analytical solution is presented for the regions close to the entrance. A parametric study reveals that increasing amounts of the Peclet number result in higher wall heat fluxes, whereas the opposite is true for the flow behavior index. Furthermore, based on the value of the dimensionless Joule heating parameter, the Nusselt number may be either an increasing or a decreasing function of the axial coordinate or even both of them in the presence of a singularity point. The viscous heating effects are also found to be negligible.