Electro-osmotic Flow Of Viscoelastic Fluid Research Articles

Numerical Study of the Time-Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel.

Electroosmotic flow (EOF) is of utmost significance due to its numerous practical uses in controlling flow at micro/nanoscales. In the present study, the time-periodic EOF of a viscoelastic fluid is statistically analyzed using a short 10:1 constriction microfluidic channel joining two reservoirs on either side. The flow is modeled using the Oldroyd-B (OB) model and the Poisson-Boltzmann model. The EOF of a highly concentrated polyacrylamide (PAA) aqueous solution is investigated under the combined effects of an alternating current (AC) electric field and a direct current (DC) electric field. Power-law degradation is visible in the energy spectra of the velocity fluctuations over a wide frequency range, pointing to the presence of elastic instabilities in the EOF. The energy-spectra curves of the velocity fluctuations under a DC electric field exhibit peaks primarily beneath 20 Hz, with the greatest peak being observed close to 6 Hz. When under both DC and AC electric fields, the energy spectra of the velocity fluctuations exhibit a peak at the same frequency as the AC electric field, and the highest peak is obtained when the frequency of the AC electric field is near 6 Hz. Additionally, the frequency of the AC electric field affects how quickly the viscoelastic EOF flows. Higher flow rates are obtained at relatively low frequencies compared to under the DC electric field, and the greatest flow rate is found close to 6 Hz. But as the frequency rises further, the flow rate falls. The flow rate falls to a level below the DC electric field when the frequency is sufficiently high.

Transient Analysis of the Electro-Osmotic Flow of Multilayer Immiscible Maxwell Fluids in an Annular Microchannel

This work investigates the transient multilayer electro-osmotic flow of viscoelastic fluids through an annular microchannel. The dimensionless mathematical model of multilayer flow is integrated by the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, the rheological Maxwell model, initial conditions, and the electrostatic and hydrodynamic boundary conditions at liquid-liquid and solid-liquid interfaces. Although the main force that drives the movement of fluids is due to electrokinetic effects, a pressure gradient can also be added to the flow. The semi-analytical solution for the electric potential distribution and velocity profiles considers analytical techniques as the Laplace transform method, with numerical procedures using the inverse matrix method for linear algebraic equations and the concentrated matrix exponential method for the inversion of the Laplace transform. The results presented for velocity profiles and velocity tracking at the transient regime reveal an interesting oscillatory behavior that depends on elastic fluid properties via relaxation times. The time required for the flow to reach steady-state is highly dependent on the viscosity ratios and the dimensionless relaxation times. In addition, the influence of other dimensionless parameters on the flow as the electrokinetic parameters, zeta potentials at the walls, permittivity ratios, ratio of pressure forces to electro-osmotic forces, number of fluid layers, and annular thickness are investigated. The findings of this study have significant implications for the precise control of parallel fluid transport in microfluidic devices for flow-focusing applications.

Electroosmotic flow of viscoelastic fluid through a microchannel with slip-dependent zeta potential

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

Effect of magnetic field on electroosmotic flow of viscoelastic fluids in a microchannel.

Electroosmotic flow is an efficient transportation technology driven by applying an external electric field across the microchannel, which has a great potential for futureapplication. This work is presented to study the unsteady electroosmotic flow of viscoelastic fluids combined with a constant pressure gradient and a vertical magnetic field through a parallel plate microchannel. For the reason that the upper and bottom walls of the parallel plate microchannel in microfluidic devices can be made of different materials, this leads to different hydrophobic properties, asymmetric zeta wall potentials, and different slip boundary conditions. The Navier slip model with different slip coefficients at walls is considered. The generalized Maxwell fluid with fractional derivative is adopted for the constitutive equation of the fluid. The analytical and numerical solutions of velocity are derived by employing the integral transform method and finite difference method, respectively. Excellent agreement is found between the numerical solutions and analytical solutions. Finally, the effects of fractional parameter , relaxation time , slip coefficients and , the ratio of wall zeta potentials , Hartmann number , and electrical field strength parameter on velocity profiles are interpreted graphically in detail.

Electroosmotic Flow of Viscoelastic Fluid through a Constriction Microchannel

Electroosmotic flow (EOF) has been widely used in various biochemical microfluidic applications, many of which use viscoelastic non-Newtonian fluid. This study numerically investigates the EOF of viscoelastic fluid through a 10:1 constriction microfluidic channel connecting two reservoirs on either side. The flow is modelled by the Oldroyd-B (OB) model coupled with the Poisson–Boltzmann model. EOF of polyacrylamide (PAA) solution is studied as a function of the PAA concentration and the applied electric field. In contrast to steady EOF of Newtonian fluid, the EOF of PAA solution becomes unstable when the applied electric field (PAA concentration) exceeds a critical value for a fixed PAA concentration (electric field), and vortices form at the upstream of the constriction. EOF velocity of viscoelastic fluid becomes spatially and temporally dependent, and the velocity at the exit of the constriction microchannel is much higher than that at its entrance, which is in qualitative agreement with experimental observation from the literature. Under the same apparent viscosity, the time-averaged velocity of the viscoelastic fluid is lower than that of the Newtonian fluid.

Atangana–Baleanu fractional model for electro-osmotic flow of viscoelastic fluids

Abstract The main goal of the current research paper is to examine the magnetohydrodynamics (MHD) free convection flow of generalized Walters’-B fluid with the effect of electro-osmosis. Electro-osmosis is the motion of liquid across a porous material which is generated by the applied potential on a net mobile electric charge in a solution. The classical Walters’-B fluid model is transformed to generalize Walters’-B fluid model using the new idea of Atangana–Baleanu time fractional derivative. Exact solutions for the velocity and temperature profiles of the stated problem are obtained using the Laplace transform technique. Some interesting and important results have been obtained from the current study. The effects of various embedded parameters like Walters’-B parameter Γ, Prandtl number Pr, Grashof number Gr, Keff and electro-osmosis parameter Es have been plotted graphically using Mathcad software. It is worth nothing that for increasing values of Es, velocity decreases. Furthermore, a decrease in velocity is observed for increasing value of Walters’-B fluid parameter Γ.

Effect of the solvent viscosity on pure electro-osmotic flow of viscoelastic fluids

In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution (β3ɛDeκ2≤2/27), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan–Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model).

Electro-elastic instabilities in cross-shaped microchannels

Purely-elastic flow instabilities have been extensively investigated in pressure-driven systems, but little attention has been paid to electrically-driven systems. This work attempts to fill this gap by investigating the electroosmotic flow of viscoelastic fluids in cross-slot and flow-focusing micro-devices, with a special focus on the onset of elastic instabilities. Relying on the visualization of dye patterns, the onset of electro-elastic instabilities for dilute and semi-dilute polyacrylamide solutions was observed at a low bulk Weissenberg number, O(10−2), through a direct transition from a steady symmetric flow to a time-dependent asymmetric flow. Time-series analysis of the dye interface patterns revealed a broad range of excitation frequencies with a power-law decay. The elastic instabilities observed seem not to improve significantly the mixing efficiency, contrarily to what has been previously reported for unstable pressure-driven flows. Numerical simulations of the electroosmotic flows were also carried out with a finite-volume method, showing that the observed electro-elastic instabilities can be predicted numerically. Both the experimental and numerical results suggest that the large stresses developed inside the electric double layer, coupled with the streamline curvature around the geometry corners, play a fundamental role in the onset and in the dynamics of the observed electro-elastic instabilities. However, further research is needed to clarify the mechanism of electro-elastic instabilities, and, in general, to improve our understanding of the complex behavior of polymeric fluids in electroosmotic flows.

Hydrodynamic dispersion by electroosmotic flow of viscoelastic fluids within a slit microchannel

The biofluids being manipulated in lab-on-a-chip devices usually contain elastic macromolecules. Accordingly, for an accurate modeling of the relevant flow physics one should invoke viscoelastic constitutive equations. In this paper, attention is paid toward the hydrodynamic dispersion by the fully developed electroosmotic flow of PTT viscoelastic fluids in slit microchannels of low zeta potential. Adopting the Taylor–Aris approach, analytical solutions are derived for late-time solute concentration and effective dispersion coefficient. Finite element-based numerical simulations are also conducted to monitor the broadening of an analyte band from the moment of injection. Both approaches are found to be in a good agreement with an average error of below 8% in the calculated dispersion coefficients. It is observed that, for given zeta potential and electrolyte type, the hydrodynamic dispersion is severely pronounced by increasing the level of elasticity in the fluid. The variations are reversed and less pronounced when the analysis is made for a fixed mean flow rate. Moreover, the effective dispersivity grows by thickening the EDL when it is sufficiently thin, whereas the opposite is true for thick EDLs. Finally, an inspection of the average concentration reveals the formation of tails for thick EDLs that may reduce the resolution in sensing applications.

Dispersion for periodic electro-osmotic flow of Maxwell fluid through a microtube

This paper mainly studies the solute dispersion driven by the periodic oscillatory electro-osmotic flow of viscoelastic fluid described by Maxwell constitutive modeling. Series expansion and transform methods are used to solve the unsteady convection dispersion equation. Analytic expressions of the natural dispersion coefficient K(t) and the mean concentration Cm are derived. By numerical computation, the influences of several nondimensional parameters, such as electrokinetic width K, oscillating angular frequency ω of the external forced electrical field, oscillating Reynolds number Re and relaxation time De on the dispersion coefficient K(t) and mean concentration Cm are investigated. The augment in amplitude of K(t) and quick decrease of Cm reflect the enhancement of the mass transfer process. Results indicate that smaller K and ω lead to larger amplitude of K(t) and quicker reduction of Cm. Moreover, the increase in De also can magnify the amplitude of K(t) and decrease the mean concentration Cm. In addition, we find there exists a critical oscillating Reynold number Re by analyzing the variations of K(t) and Cm with Re. Finally, comparing to the case of Newtonian fluid by setting De=0, a more effective dispersion process for Maxwell fluid can be observed interestingly. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.

Influence of slip wall effect on a non-isothermal electro-osmotic flow of a viscoelastic fluid

We present an analytical model that predicts the influence of Joule heating on the slip velocity in an electro-osmotic flow (EOF) of viscoelastic fluids. The viscoelasticity of the fluid is taken into account by employing the simplified Phan-Thien and Tanner constitutive model (sPTT). The Joule heating induces temperature gradients along the microchannel making properties non-uniform and hence alters the electric potential and the flow field. In consequence, the slip velocity and the velocity gradient on the microchannel surface are drastically modified in comparison with the case of uniform properties. Using the well-known lubrication theory, the momentum equations together with the energy, Poisson and Ohmic current conservation equations are considerably simplified. The dimensionless mathematical model is solved by using a regular perturbation technique, which is compared against a numerical solution. The results show that using hydrophobic microchannels, for the used values of the parameters involved in this analysis, the volumetric flow rate through microchannels can be massively amplified in about 400%, in comparison with the case of non-slipping surfaces. In addition, by using hydrophobic microchannels, the maximum temperature in the microchannel can be substantially reduced.

Depletion of cross‐stream diffusion in the presence of viscoelasticity

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T‐sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one‐dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015

Transient electro-osmotic flow of Oldroyd-B fluids in a straight pipe of circular cross section

The transient electro-osmotic flow of viscoelastic fluids in a narrow capillary tube is examined. With the help of integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson–Boltzmann equation and the Navier–Stokes equation. It is shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The results of classical fluid, i.e., Newtonian fluid and those of Maxwell fluid and the second grade fluid can be obtained as the special cases of the results in present study. The effects of relaxation time and retardation time on the velocity profiles are analyzed numerically. It is pointed out that the electro-osmotic flow of viscoelastic fluids is more difficult to achieve the steady state.

Electroosmotic flows of viscoelastic fluids with asymmetric electrochemical boundary conditions

The electroosmotic flow of viscoelastic fluids is studied analytically by using the Phan-Thien Tannar (PTT) constitutive model. Unidirectional steady-state flow is formed in a two-dimensional microchannel bounded by two parallel plates with different zeta potentials or by a plane substrate and a free surface. The exact flow field is obtained based on first principles. Velocity profiles and flow rates are studied parametrically by varying relaxation time, extensibility parameter and slip parameter of the PTT model and the electrochemical properties of the liquid and the bounding plates. Comparisons are made with Newtonian fluids and previous non-Newtonian analyses.

Heat transfer due to electroosmotic flow of viscoelastic fluids in a slit microchannel

The bio-microfluidic systems are usually encountered with non-Newtonian behaviors of working fluids. The rheological behavior of some bio-fluids can be described by differential viscoelastic constitutive equations that are related to PTT and FENE-P models. In the present work, thermal transport characteristics of the steady fully developed electroosmotic flow of these fluids in a slit microchannel with constant wall heat fluxes have been investigated. The Debye–Huckel linearization is adopted and the effects of viscous dissipation and Joule heating are taken into account. Analytical solutions are obtained for the transverse distributions of velocity and temperature and finally for Nusselt number. Two different behaviors are observed for the Nusselt number variations due to increasing ϵ geWe 2 which are an increasing trend for positive wall heat flux and a decreasing one for negative wall heat flux. However, the influence of ϵ geWe 2 on Nusselt number vanishes at higher values of the dimensionless Debye–Huckel parameter. It is also realized that the effect of viscous heating is more important at small values of both ϵ geWe 2 and the dimensionless Debye–Huckel parameter. Furthermore, the results show a singularity in Nusselt number at higher negative values of the dimensionless Joule heating parameter.

Electro-osmotic flow of viscoelastic fluids in microchannels under asymmetric zeta potentials

The flow of viscoelastic fluids between parallel plates under the combined influence of electro-osmotic and pressure gradient forcings with asymmetric boundary conditions, by considering different zeta potentials at the walls, is investigated. The fluids are z-z symmetric electrolytes. The analytic solutions of the electrical potential, velocity distributions and streaming potential are based on the Debye-Huckel approximation for weak potential. The viscoelastic fluids used are modelled by the simplified Phan-Thien-Tanner constitutive equation, with linear kernel for the stress coefficient function, and the Finitely Extensible Nonlinear Elastic dumbbells model with a Peterlin approximation for the average spring force. The combined effects of fluid rheology, electrical double- layer thickness, ratio of the wall zeta potentials and ratio between the applied streamwise gradients of electrostatic potential and pressure on the fluid velocity and stress distributions are discussed.

Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels

Transient electro-osmotic flow of viscoelastic fluids in rectangular micro-channels is investigated. The general twofold series solution for the velocity distribution of electro-osmotic flow of viscoelastic fluids with generalized fractional Oldroyd-B constitutive model is obtained by using finite Fourier and Laplace transforms. Under three limiting cases, the generalized Oldroyd-B model simplifies to Newtonian model, fractional Maxwell model and generalized second grade model, where all the explicit exact solutions for velocity distribution are found through the discrete Laplace transform of the sequential fractional derivatives. These exact solutions may be able to predict the flow behavior of viscoelastic biological fluids in BioMEMS and Lab-on-a-chip devices and thus could benefit the design of these devices.