Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel

Many lab-on-a-chip based microsystems process biofluids such as blood and DNA solutions. These fluids are viscoelastic and show extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. In the present paper, we investigate viscoelastic electroosmotic flows through a rectangular straight microchannel with and without pressure gradient. It is shown that the volumetric flow rates of viscoelastic fluids are significantly different from those of Newtonian fluids under the same external electric field and pressure gradient. Moreover, when pressure gradient is imposed on the microchannel there appear appreciable secondary flows in the viscoelastic fluids, which is never possible for Newtonian laminar flows through straight microchannels. The retarded or enhanced volumetric flow rates and secondary flows affect dispersion of solutes in the microchannel nontrivially.     

Analysis of electroosmotic flow of power-law fluids in a slit microchannel

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.     

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier-Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye-Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.     

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.     

Simultaneous estimation of zeta potential and slip coefficient in hydrophobic microchannels

Electroosmotic flows through hydrophobic microchannels experience velocity slip at the channel wall, which increases the volumetric flow rate at a given electric potential gradient. The conventional method of zeta potential estimation using the volumetric flow rate may yield quite inaccurate zeta potential unless the velocity slip is appropriately taken care of. In the present investigation we develop a method for simultaneous estimation of zeta potential and velocity slip coefficient in the electroosmotic flow through a hydrophobic microchannel using velocity measurements. The relevant inverse problem is solved through the minimization of a performance function utilizing a conjugate gradient method. The present method is found to estimate the zeta potential and slip coefficient accurately even with noisy velocity measurements.     

Expressions for evaluating the possibility of slip at the liquid-solid interface in open tube capillary electrochromatography

In this work, expressions are constructed and solved that describe the velocity field of electroosmotic flow (EOF) in open tube capillary electrochromatography (CEC) systems when the possibility of having unequal tangential velocities at the liquid-solid interface is considered and a slip condition is employed as a boundary condition for the velocity of the EOF at the capillary wall. The coupled equations of hydrodynamics (momentum balance equation) and electrostatics (Poisson equation) are solved numerically in order to obtain the distribution of the velocity field as well as the value of the volumetric flow rate in the open tube. Also, expressions for the velocity field and the volumetric flow rate of the EOF are presented that are valid for certain electrolytic systems and for certain parameter values for which analytical solutions to the momentum balance and Poisson equations could be obtained. The results presented in this work indicate that having slip in the velocity of the EOF at the wall of the capillary could (i) substantially increase the electroosmotic velocity in the plug-flow region of the radial domain of the open capillary tube and (ii) increase the portion of the radial domain of the open capillary tube where the velocity of the EOF has a plug-flow profile, which in turn could increase the average velocity and volumetric flow rate of the EOF in the open capillary tube. Furthermore, the modeling approach and the results presented in this work indicate a method for experimentally evaluating the possibility of having slip in the velocity of the EOF at the capillary wall.     

Electroosmotic Flow through an Annulus

The electro-osmosis through an annulus is investigated. The electric potential and flow velocity profile are obtained by solving the linearized Poisson-Boltzmann equation and the Stokes equation. Both the thin and thick double layer limits are analyzed. Under the condition of thin double layer, the electro-osmotic mobility can be described by the Helmholtz-Smoluchowski equation with a geometry-dependent correction factor. There exist net flows even for zero area-averaged surface charge density due to the curvature differences between the inner and outer walls. The flow direction is determined by the sign of the charge on the inner cylinder. We also found that under certain circumstances the flow direction in an annulus is opposite to that in a capillary with the same sign of the net charge. Copyright 2000 Academic Press.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Electroosmotic flow of non‐Newtonian fluids in a constriction microchannel

Insulator‐based dielectrophoresis has to date been almost entirely restricted to Newtonian fluids despite the fact that many of the chemical and biological fluids exhibit non‐Newtonian characteristics. We present herein an experimental study of the fluid rheological effects on the electroosmotic flow of four types of polymer solutions, i.e., 2000 ppm xanthan gum (XG), 5% polyvinylpyrrolidone (PVP), 3000 ppm polyethylene oxide (PEO), and 200 ppm polyacrylamide (PAA) solutions, through a constriction microchannel under DC electric fields of up to 400 V/cm. We find using particle streakline imaging that the fluid elasticity does not change significantly the electroosmotic flow pattern of weakly shear‐thinning PVP and PEO solutions from that of a Newtonian solution. In contrast, the fluid shear‐thinning causes multiple pairs of flow circulations in the weakly elastic XG solution, leading to a central jet with a significantly enhanced speed from before to after the channel constriction. These flow vortices are, however, suppressed in the strongly viscoelastic and shear‐thinning PAA solution.     

Electroosmotic Flows Created by Surface Defects in Capillary Electrophoresis

We compute the electroosmotic flow in nonuniformly charged planar and cylindrical capillaries for the limit of low-Reynolds-number flows and thin Debye layers. Analytical formulae for the velocity field are provided for the general case of an arbitrary surface inhomogeneity but we also focus on various specific defect geometries. Many important features can be obtained from the simple lubrication approximation. The pressure jump induced by the presence of such surface defects is calculated and the possible occurrence of recirculating flows is discussed, as are effects of the flow perturbations on dispersion in capillary electrophoresis. Copyright 1999 Academic Press.     

Spreadsheet analysis of the field-driven start-up flow in a microfluidic channel

We discuss, in this article, the solution method of the unsteady electroosmotic flow of Newtonian fluid in a square microfluidic channel cross-section in the framework of spreadsheet analysis. We demonstrate the implementation of the finite difference scheme, which is used for the discretization of the transport equations governing the flow dynamics of the present problem, in the spreadsheet tool. Also, we have shown the implementation details of different boundary conditions, which are typically used for the underlying electrohydrodynamics in a microfluidic channel, in the spreadsheet analysis tool. We show that the results obtained from the spreadsheet analysis match accurately with the numerical solutions for both the electrostatic potential distribution and the flow velocity. Our results of this analysis justify the credibility of the spreadsheet tool for capturing the intricate details of the electrically actuated microflows during the initial transiences, that is, for the start-up flows and the phenomenon due to the electrical double layer effect, quite effectively. The inferences of this analysis will open up a new research paradigm of microfluidics and microscale transport processes by providing the potential applicability of the spreadsheet tools to obtain the flow physics of our interest in a very intuitive and less expensive manner.     

Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

Experimental investigation of bubble and drop formation at submerged orifices

The aim of this study was to investigate bubble/drop formation at a single submerged orifice in stagnant Newtonian fluids and to gain qualitative understanding of the formation mechanism. The effects of various governing parameters were studied. Formation behavior of bubbles and drops in Newtonian aqueous solutions were investigated experimentally under different operating conditions with various orifices. The results show that the volume of the detached dispersed phase (bubble or drop) increases with the viscosity of the continuous phase (or dispersion medium), surface tension, orifice diameter, and dispersed phase flow rate. A PIV system was employed to measure the velocity flow field quantitatively during the bubble/drop formation, giving interesting information useful for the elucidation of the fundamental formation process at the orifice. It was revealed that the orifice shape strongly influences the size of the bubble formed. Furthermore, based on a simple mass balance, a general correlation successfully predicting both bubble and drop sizes has been proposed.     

Numerical study of electroosmotic slip flow of fractional Oldroyd-B fluids at high zeta potentials

In this paper, an investigation of the electroosmotic flow of fractional Oldroyd-B fluids in a narrow circular tube with high zeta potential is presented. The Navier linear slip law at the walls is considered. The potential field is applied along the walls described by the nonlinear Poisson–Boltzmann equation. It's worth noting here that the linear Debye–Hückel approximation can't be used at the condition of high zeta potential and the exact solution of potential in cylindrical coordinates can't be obtained. Therefore, the Matlab bvp4c solver method and the finite difference method are employed to numerically solve the nonlinear Poisson–Boltzmann equation and the governing equations of the velocity distribution, respectively. To verify the validity of our numerical approach, a comparison has been made with the previous work in the case of low zeta potential and the excellent agreement between the solutions is clear. Then, in view of the obtained numerical solution for the velocity distribution, the numerical solutions of the flow rate and the shear stress are derived. Furthermore, based on numerical analysis, the influence of pertinent parameters on the potential distribution and the generation of flow is presented graphically.     

Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.     

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.     

Flow of non‐newtonian fluids in porous media

The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.