Wall Zeta Potential Research Articles

Electroosmotic flow of Phan-Thien–Tanner fluids at high zeta potentials: An exact analytical solution

We present a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis. We use the simplified Phan-Thien–Tanner (s-PTT) constitutive relationships to describe the rheological behavior of the viscoelastic fluid, while Navier’s slip law is employed to model the interfacial hydrodynamic slip. Here, we derive analytical solutions for the potential distribution, flow velocity, and volumetric flow rate based on the complete Poisson–Boltzmann equation (without considering the frequently used Debye–Hückel linear approximation). For the underlying electrokinetic transport, this investigation primarily reveals the influence of fluid rheology, wall zeta potential as modulated by the interfacial electrochemistry and interfacial slip on the velocity distribution, volumetric flow rate, and fluid stress, as well as the apparent viscosity. We show that combined with the viscoelasticity of the fluid, a higher wall zeta potential and slip coefficient lead to a phenomenal enhancement in the volumetric flow rate. We believe that this analysis, besides providing a deep theoretical insight to interpret the transport process, will also serve as a fundamental design tool for microfluidic devices/systems under electrokinetic influence.

Pulsatile electroosmotic flow in a microchannel with asymmetric wall zeta potentials and its effect on mass transport enhancement and mixing

In this work, we analyze theoretically the mass transport of a neutral solute in a pulsatile electroosmotic flow (PEOF), circulating in a parallel flat plate microchannel whose walls are characterized by asymmetric zeta potentials. The microchannel is connected to a two reservoirs having different concentrations. To analyze the mass transport in the PEOF, the Debye-Hückel approximation is assumed, and the electric potential in the Debye length is obtained from the Poisson-Boltzmann equation. Then, using the momentum and concentration equations, the flow and concentration fields are analytically determined for the periodic stage. Such field distributions depend principally on three dimensionless parameters: an angular Reynolds number, the Schmidt number, and the ratio between the half height of the channel and the Debye length. For obtaining insight on the physical aspects of the studied phenomenon, an asymptotic solution is additionally obtained in the limits of small and large values of the angular Reynolds number. Some important results derived from this analysis show the conditions for which the mass transport of a neutral solute can be enhanced and the circumstances whereby mixing of species is achieved.

Pulsatile electroosmotic flow of a Maxwell fluid in a parallel flat plate microchannel with asymmetric zeta potentials

The pulsatile electroosmotic flow (PEOF) of a Maxwell fluid in a parallel flat plate microchannel with asymmetric wall zeta potentials is theoretically analyzed. By combining the linear Maxwell viscoelastic model, the Cauchy equation, and the electric field solution obtained from the linearized Poisson-Boltzmann equation, a hyperbolic partial differential equation is obtained to derive the flow field. The PEOF is controlled by the angular Reynolds number, the ratio of the zeta potentials of the microchannel walls, the electrokinetic parameter, and the elasticity number. The main results obtained from this analysis show strong oscillations in the velocity profiles when the values of the elasticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.

Dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid through a microchannel with a slowly varying wall zeta potential

The dispersion coefficient of a passive solute in a steady-state pure electro-osmotic flow (EOF) of a viscoelastic liquid, whose rheological behaviour follows the simplified Phan-Thien–Tanner (sPTT) model, along a parallel flat plate microchannel, is studied. The walls of the microchannel are assumed to have modulated and low $\unicode[STIX]{x1D701}$ potentials, which vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient was solved using the lubrication approximation theory (LAT). The solution of the electric potential is based on the Debye–Hückel approximation for a symmetric $(z:z)$ electrolyte. The viscoelasticity of the fluid is observed to notably amplify the axial distribution of the effective dispersion coefficients due to the variation in the $\unicode[STIX]{x1D701}$ potentials of the walls. The problem was formulated for two cases: when the Debye layer thickness (EDL) was on the order of unity (thick EDL) and in the limit where the thickness of the EDL was very small compared with the height of the microchannel (thin EDL limit). Due to the coupling between the nonlinear governing equations and the sPTT fluid model, they were replaced by their approximate linearized forms and solved in the limit of $\unicode[STIX]{x1D700}\ll 1$ using the regular perturbation technique. Here $\unicode[STIX]{x1D700}$ is the amplitude of the sinusoidal function of the $\unicode[STIX]{x1D701}$ potentials. Additionally, the numerical solution of the simplified governing equations was also obtained for $\unicode[STIX]{x1D700}=O(1)$ and compared with the approximate solution, showing excellent agreement for $0\leqslant \unicode[STIX]{x1D700}\leqslant 0.3$. Note that the dispersion coefficient primarily depends on the Deborah number, on the ratio of the half-height of the microchannel to the Debye length, and on the assumed variation in the $\unicode[STIX]{x1D701}$ potentials of the walls.

Electroosmotic flow of a two-layer fluid in a slit channel with gradually varying wall shape and zeta potential

This study aims to investigate electroosmotic (EO) flow of a two-layer fluid through a slit microchannel where the wall shape as well as zeta potential may vary slowly and periodically with axial position. The two-layer EO flow is a model for the flow of two immiscible fluids: a non-conducting working fluid being dragged into motion by a conducting sheath fluid. Electric double layers may develop in the conducting fluid near the interface between the two fluids, and near a wall that is assumed to be non-uniform in both shape and zeta potential distribution. Because of these geometrical and electrical non-uniformities, pressure is internally induced. The two-fluid flow is therefore driven by electrokinetic and hydrodynamic forcings, while subjected to the combined effects of the axial variations of the wall shape and potential distribution. The present problem is formulated by invoking the lubrication approximation, for a nearly parallel flow of low Reynolds number, and the governing equations are solved as analytically as possible. The induced pressure gradient and the deformed shape of the interface, which are functions of axial position, as well as the flow rates of the two fluids, are determined by an iterative trial-and-error numerical scheme. Results are generated to show the effects due to various factors, including the applied pressure difference, interfacial potential, viscosity ratio, wall undulation, and phase shift between the wall shape and potential distribution. Some of the effects on flow in a non-uniform channel can be qualitatively different from that in a uniform channel.

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclet number and Debye–Huckel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.

Hydrodynamic dispersion in a combined magnetohydrodynamic- electroosmotic-driven flow through a microchannel with slowly varying wall zeta potentials

The effective dispersion coefficient of a neutral solute in the combined electroosmotic (EO) and magnetohydrodynamic (MHD)-driven flow of a Newtonian fluid through a parallel flat plate microchannel is studied. The walls of the microchannel are assumed to have modulated and low zeta potentials that vary slowly in the axial direction in a sinusoidal manner. The flow field required to obtain the dispersion coefficient is solved using the lubrication approximation theory. The solution of the electrical potential is based on the Debye-Hückel approximation for a symmetric (Z:Z) electrolyte solution. The EO and MHD effects, together with the variations in the zeta potentials of the walls, are observed to notably modify the axial distribution of the effective dispersion coefficient. The problem is formulated for two cases of the zeta potential function. Note that the dispersion coefficient primarily depends on the Hartmann number, on the ratio of the half height of the microchannel to the Debye length, and on the assumed variation in the zeta potentials of the walls.

Startup electroosmotic flow of a viscoelastic fluid characterized by Oldroyd-B model in a rectangular microchannel with symmetric and asymmetric wall zeta potentials

We study the startup flow of a viscoelastic fluid in a microfluidic channel, by considering the Oldroyd-B constitutive model. In particular, we aim to capture the confluence of the interfacial charge and the combined viscous and elastic properties of the fluid toward dictating the resulting startup flow characteristics. We further highlight the implications in the asymmetric nature of the wall zeta potentials on the flow behavior. We observe an increase in flow rate with increase in elastic nature of the fluid for studies with symmetric wall zeta potentials. For cases with asymmetric zeta potentials, we observe large movement of the velocity peaks, creating crests and troughs. Results from the present study may turn out to be useful in designing lab on a chip based microfluidic devices transporting bio-fluids such as blood, saliva and mucus by means of electroosmotic mechanisms.

Computer modelling of electro-osmotically augmented three-layered microvascular peristaltic blood flow

A theoretical study is presented here for the electro-osmosis modulated peristaltic three-layered capillary flow of viscous fluids with different viscosities in the layers. The layers considered here are the core layer, the intermediate layer and the peripheral layer. The analysis has been carried out under a number of physical restrictions viz. Debye-Hückel linearization (i.e. wall zeta potential ≤25mV) is assumed sufficiently small, thin electric double layer limit (i.e. the peripheral layer is much thicker than the electric double layer thickness), low Reynolds number and large wavelength approximations. A non-dimensional analysis is used to linearize the boundary value problem. Fluid-fluid interfaces, peristaltic pumping characteristics, and trapping phenomenon are simulated. Present study also evaluates the responses of interface, pressure rise, time-averaged volume flow rate, maximum pressure rise, and the influence of Helmholtz-Smoluchowski velocity on the mechanical efficiency (with two different cases of the viscosity of fluids between the intermediate and the peripheral layer). Trapping phenomenon along with bolus dynamics evolution with thin EDL effects are analyzed. The findings of this study may ultimately be useful to control the microvascular flow during the fractionation of blood into plasma (in the peripheral layer), buffy coat (intermediate layer) and erythrocytes (core layer). This work may also contributes in electrophoresis, hematology, electrohydrodynamic therapy and, design and development of biomimetic electro-osmotic pumps.

Low-Cost Zeta Potentiometry Using Solute Gradients.

The zeta potential is an electric potential in the Debye screening layer of an electrolyte, which represents a key physicochemical surface property in various fields ranging from electrochemistry to pharmaceuticals. Thus, characterizing the zeta potential is essential for many applications, but available measurement techniques are limited. Electrophoretic light scattering is typically used to measure the zeta potential of particles in suspension, whereas zeta potential measurements of a solid wall in solution rely on either streaming potential or electroosmotic mobility measurement techniques, both of which are expensive and sophisticated. Here, a simple, robust method to simultaneously measure the zeta potential of particles in suspension and solid walls is presented. The method uses solute gradients to induce particle and fluid motions via diffusiophoresis and diffusioosmosis, respectively, which are both sensitive to the zeta potential of the particle and the wall. By visualizing the particle dynamics, both zeta potentials can be determined independently. Finally, a compact microscope is used to demonstrate low-cost zeta potentiometry that allows measurement of both particle and wall zeta potentials, which suggests a cost-effective tool for pharmaceuticals as well as for educational purposes.

Pure axial flow of viscoelastic fluids in rectangular microchannels under combined effects of electro-osmosis and hydrodynamics

This paper presents an analysis of the combined electro-osmotic and pressure-driven axial flows of viscoelastic fluids in a rectangular microchannel with arbitrary aspect ratios. The rheological behavior of the fluid is described by the complete form of Phan-Thien–Tanner (PTT) model with the Gordon–Schowalter convected derivative which covers the upper convected Maxwell, Johnson–Segalman and FENE-P models. Our numerical simulation is based on the computation of 2D Poisson–Boltzmann, Cauchy momentum and PTT constitutive equations. The solution of these governing nonlinear coupled set of equations is obtained by using the second-order central finite difference method in a non-uniform grid system and is verified against 1D analytical solution of the velocity profile with less than 0.06% relative error. Also, a parametric study is carried out to investigate the effect of channel aspect ratio (width to height), wall zeta potential and the Debye–Huckel parameter on 2D velocity profile, volumetric flow rate and the Poiseuille number in the mixed EO/PD flows of viscoelastic fluids with different Weissenberg numbers. Our results show that, for low channel aspect ratios, the previous 1D analytical models underestimate the velocity profile at the channel half-width centerline in the case of favorable pressure gradients and overestimate it in the case of adverse pressure gradients. The results reveal that the inapplicability of the Debye–Huckel approximation at high zeta potentials is more significant for higher Weissenberg number fluids. Also, it is found that, under the specified values of electrokinetic parameters, there is a threshold for velocity scale ratio in which the Poiseuille number is approximately independent of channel aspect ratio.

ANALYTICAL STUDY OF ELECTRO-OSMOSIS MODULATED CAPILLARY PERISTALTIC HEMODYNAMICS

A mathematical model is developed to analyze electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye–Hückel linearization (i.e., wall zeta potential [Formula: see text] 25[Formula: see text]mV) is sufficiently small). The transformed, nondimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e., where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz–Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps.

Pressure driven transport of neutral macro-solute in microchannel with porous wall at high surface potential

Mass transport of macro-solutes under streaming potential in a microchannel with porous wall is presented in this study. The streaming field under high wall potential and overlapping electric double layer with coupled velocity and concentration of neutral solutes is computed numerically in this work. Streaming potential increases by 7 folds as κH decreases from 0.7 to 0.1 at ζ=-50mV, where, κ-1 is Debye length, H is channel half height and ζ is wall zeta potential. Mass transport in terms of Sherwood number is calculated including osmotic effect of the solution and selective retention of macrosolutes. Electroviscous effects resulting from streaming potential and overlapping electric double layer at higher wall zeta potential have significant effect on velocity field and the mass transport of macrosolutes. Apparent viscosity due to this effect increases upto 3.2 times the solution viscosity at κH=0.2 for ζ=-50mV. This effect is intensified upto 4 times at higher wall potential, ζ=-200mV at κH=0.5. At these points, the velocity profile suffers the most adversely affecting the mass transfer reducing Sherwood number to 4 (about 5 times reduction compared to higher κH) at ζ=-200mV and κH=0.5. Sherwood number reduces by three to four folds at the critical κH values, representing the minimum. The induced electrical field due to the streaming potential is higher compared to axial pressure drop for |ζ|>50mV at κH<0.3. The electric double layer overlaps for the values of κH upto 0.7 corresponding to ζ=-50mV. In case of high ζ (−200mV), the centerline potential can be as high as 75% of the wall potential for κH=1.5. The minimum wall Peclet number (Pew‾) occurs at κH=0.5 for ζ=-200mV, which is five times less than the situation without electrokinetic effects.

Electroosmotic flow of a power law fluid in an elliptic microchannel

Abstract In this paper the two dimensional electroosmotic flow of a non-Newtonian fluid governed by the power law model is studied for circular and elliptic microchannels. The electric potential and the velocity distribution inside the microchannel are solved without invoking the Debye–Huckel linear approximation. The solutions are sought for different aspect ratio (E), power law index (n), Debye–Huckel parameter (K) and the wall zeta potential (ζ). The effect of these parameters is studied on the ratio of flow rates Q/Qcir and friction parameter. The comparison of a circular geometry (E = 1) and an elliptical geometry (E ≠ 1) is made on an equal cross sectional area basis. Elliptic microchannels always reduce the flow rate when compared to circular microchannels. This reduction is much more significant at lower values of K and ζ. Shear thickening fluids affect the reduction in flow rates much more when compared to shear thinning ones. This reduction in flow rates becomes larger as the aspect ratio increases. The frictional parameter increases with K and ζ for all E. Shear thickening fluids have larger frictional parameter values compared to shear thinning fluids.

Numerical Simulation of Heat Transfer in Mixed Electroosmotic Pressure-Driven Flow in Straight Microchannels

This paper investigates two-dimensional, time-independent elecroosmotic pressure-driven flow generated by a direct current electric potential with asymmetrical and symmetrical zeta potential distributions along the microchannel walls. Fluid flow through the horizontal microchannel is simulated using a numerical method. Two different cases are proposed to study the effect of electric potential on the flow field. First, negative electric potential is applied on the microchannel walls. In this case, large segments with negative electric potential are initially placed on the first half of the microchannel walls with two different arrangements. Afterward, smaller segments with negative electric potential are placed on the microchannel walls. Next, negative electric potential is replaced by positive electric potential on the microchannel walls in the similar manner. It is shown that applying positive potential on the walls contributes to the localized circular flows within the microchannel. The size of these vortices is also proved to considerably vary with the applied zeta potential magnitude. Finally, the effect of wall zeta potential on heat transfer was studied for all the four types of microchannels by imposing a constant uniform heat flux on the walls. The Nusselt number plots indicate how heat transfer varies along the microchannel walls. The Nusselt number fluctuation can be observed where the positive and negative electric potentials are located.

Electrophoretic mobility of a spherical nanoparticle in a nanochannel

Numerical simulation is used to calculate accurately the electrophoretic mobility of a charged spherical nanoparticle confined in a nanochannel, under a weakly applied electric field. Classic models for electrophoretic mobility are valid only in the linear regime of small particle zeta potential, and for an unbounded fluid domain. However, these models fail to predict the electrophoretic mobility measured experimentally in bounded nanochannels. We adopt asymptotically expanded formulations and solve the fully coupled equations on a 3D finite element domain. Factors affecting particle mobility include electrolyte concentration, channel size, and zeta potentials on both the particle surface and channel walls. Specifically, spherical particles are examined with diameters 2a = 10 and 50 nm, in a 100 nm high channel. The non-dimensional electric double layers were varied between 0.1 &amp;lt; κa &amp;lt; 100. The results indicate that the mobility of a particle located at the nanochannel centerline agrees to within 1% of the average mobility of a particle distributed transversely throughout the nanochannel. Furthermore, confinement by the nanochannel walls was found to affect greatly nanoparticle mobility. As a result, it is feasible to use nanochannels to separate two different size nanoparticles, even when the particles have equal zeta potentials. Finally, a new method is proposed to estimate accurately particle and wall zeta potentials by contrasting the observed differences in mobility between observed in two different height channels.

Combined electroosmotic and pressure driven flow in a microchannel at high zeta potential and overlapping electrical double layer

A mathematical model for combined electroosmotic and pressure driven flow in a rectangular microchannel at high zeta potential and overlapping electrical double-layer is presented. The potential distribution is solved numerically without Debye–Hückel approximation using site dissociation model. The corresponding hydrodynamic analysis along with the associated heat transfer problem was performed. For wall potential of 120 mv, the centerline potential could be 95% of wall potential at non-dimensional channel height κa = 0.3 and it was 90% for κa = 1.0, where κ−1 is Debye length and a is half height of the channel. Centerline potential was 84% of wall potential at pH 5.5 and beyond pH 6.5, centerline potential was close to zero, even at lower value of κa (=0.3). Centerline velocity decreases by 16% as κa decreases from 1 to 0.5, when both pressure driven flow and electroosmotic flow are equally dominant, for non-dimensional zeta potential α = 3 (77 mV). For ratio of Joule heating to surface cooling beyond 5, the non-dimensional temperature in the channel is always positive. In absence of Joule heating (G = 0), Nusselt number decreases by 28% as κa decreases from 1 to 0.5. Nusselt number also decreases by 34% with increase in non-dimensional wall zeta potential from 3 to 5.

Numerical study of mixing and heat transfer in mixed electroosmotic/pressure driven flow through T-shaped microchannels

This paper investigates mixing and heat transfer characteristics of mixed electroosmotic–pressure driven flow within a T-shaped microchannel. Two different mechanisms were proposed to enhance mixing efficiency within the channel. First, a non-uniform DC electric potential was embedded on the horizontal section of the channel which causes the straight streamlines to deviate and thus increases interfacial contact area and mass diffusion by absorbing ions into electrodes. Next, a ribbed channel configuration was proposed. It is shown that due to separation, recirculation zones appear behind the obstacles which helps in enhancing mixing efficiency. Finally a combined effect of ribbed channel and wall zeta potential was investigated. The numerical results show that due to presence of non-uniform zeta potential, the induced vortices are pushed into the middle of the channel and thus mixing enhances drastically by using this scheme. Intensity of mixing was computed for all cases and it was found that for any Reynolds number, there exists a Schmidt number value which below that specific value, imposing electric field reduces mixing. Finally, heat transfer was studied for all introduced cases for a constant uniform heat flux imposed at the walls. The obtained local average Nusselt number indicates that employing zeta potential has an important effect on the mixture temperature within the channel and at the outlet of the channel.

Electrokinetic diffusioosmosis of viscoelastic Phan-Thien–Tanner liquids in slit microchannels

This research presents a theoretical/numerical investigation on electrokinetic diffusioosmotic flows of viscoelastic Phan-Thien–Tanner liquids in slit microchannels subjected to general wall zeta potentials. Based on a unidirectional lubricating flow analysis, numerical solutions to the effective viscosity, first normal stress difference, flow velocity field, and volume flow rate are obtained and expressed in terms of the spatial coordinate, half channel width to Debye length ratio, diffusivity difference parameter, wall zeta potential, and a combined elongation viscosity and Deborah number parameter (in short, Deborah number). Results of our parametric studies show that the respective strengths of the shear thinning and normal stress effects can be increased as the Deborah number is increased. Moreover, the respective strengths of the flow velocity and volume flow rate are increased as the Deborah number is increased regardless of the flow velocity and flow rate being directed towards upstream or downstream. Finally, based on the diffusivity difference parameter and zeta potential parametric pairs, the parametric regimes available for the volume flow rate to be directed towards downstream (upstream) are increased (reduced) as the value of the Deborah number parameter is reduced.

Wall polymer depletion effects on electrokinetic diffusioosmosis of power-law liquids in cylindrical capillaries

We investigate electrokinetic diffusioosmotic flows of power-law liquids including the effects of a polymer-depleted Newtonian liquid layer near the wall boundaries in circular cylindrical capillaries. Semi-analytical solutions to the flow velocity distribution and volume flow rate are obtained for conditions involving finite double layer effects on the induced electric field of the electrokinetic diffusioosmosis. Results show that the flow behavior and responses of the electrokinetic diffusioosmotic flow depend not only on the wall zeta potential, diffusivity difference parameter, and flow behavior index, but also on the depletion layer thickness to Debye thickness ratio, the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer, as well as the exact numeric values of the flow consistency parameter and the Newtonian viscosity. Including the Newtonian depletion layer gives rise to wiggled-shaped zero flow rate border curves on the zeta potential versus diffusivity difference parameter map when the depletion layer thickness to Debye thickness ratio and the ratio of the flow consistency parameter of the power-law liquid core to the viscosity of the Newtonian depletion layer are close to one. These results are not identified in previous Newtonian or non-Newtonian electrokinetic diffusioosmosis literature and may likely open new possibilities and suggest new ideas in the analysis and design of diffusiophoretic separation and diffusioosmotic flow operations.