Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

Numerical Simulation of Electroosmotic Flow near Earthworm Surface

The electroosmotic flow near an earthworm surface is simulated numerically to further understand the anti soil adhesion mechanism of earthworm. A lattice Poisson method is employed to solve electric potential and charge .distributiorts in the electric double layer along the earthworm surface. The external electric field is obtained by solving a Laplace equation. The electroosmotic flow controlled by the Navier-Stokes equations with external body force is simulated by the lattice Boltzmann method. A benchmark test shows that accurate electric potential distributions can be obtained by the LPM. The simulation shows that the moving vortices, which probably contribute to anti soil adhesion, are formed near earthworm body surface by the nonuniform and variational electrical force.

Rotating electroosmotic flow of an Eyring fluid

A perturbation analysis is presented in this paper for the electroosmotic (EO) flow of an Eyring fluid through a wide rectangular microchannel that rotates about an axis perpendicular to its own. Mildly shear-thinning rheology is assumed such that at the leading order the problem reduces to that of Newtonian EO flow in a rotating channel, while the shear thinning effect shows up in a higher-order problem. Using the relaxation time as the small ordering parameter, analytical solutions are deduced for the leading- as well as first-order problems in terms of the dimensionless Debye and rotation parameters. The velocity profiles of the Ekman-electric double layer (EDL) layer, which is the boundary layer that arises when the Ekman layer and the EDL are comparably thin, are also deduced for an Eyring fluid. It is shown that the present perturbation model can yield results that are close to the exact solutions even when the ordering parameter is as large as order unity. By this order of the relaxation time parameter, the enhancing effect on the rotating EO flow due to shear-thinning Eyring rheology can be significant.

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-Hiickel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and rnicrorotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

Electroosmotic flow of Eyring fluid in slit microchannel with slip boundary condition

In consideration of the electroosmotic flow in a slit microchannel, the con-stitutive relationship of the Eyring fluid model is utilized. Navier＇s slip condition is used as the boundary condition. The governing equations are solved analytically, yielding the velocity distribution. The approximate expressions of the velocity distribution are also given and discussed. Furthermore, the effects of the dimensionless parameters, the electrokinetic parameter, and the slip length on the flow are studied numerically, and appropriate conclusions are drawn.

Analysis of Transient Pulse Electroosmotic Flow of Maxwell Fluid through a Circular Micro-Channel Using Laplace Transform Method

A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time , especially for the smaller pulse width a. However, as the pulse width a increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time and pulse width a.

On the time development of dispersion in electroosmotic flow througha rectangular channel

This is an analytical study on the time develop- ment of hydrodynamic dispersion of an inert species in elec- troosmotic flow through a rectangular channel. The objec- tive is to determine how the channel side walls may affect the dispersion coefficient at different instants of time. To this end, the generalized dispersion model, which is valid for short and long times, is employed in the present study. An- alytical expressions are derived for the convection and dis- persion coefficients as functions of time, the aspect ratio of the channel, and the Debye-Htickel parameter representing the thickness of the electric double layer. For transport in a channel of large aspect ratio, the dispersion may undergo several stages of transience. The initial, fast time develop- ment is controlled by molecular diffusion across the narrow channel height, while the later, slower time development is governed by diffusion across the wider channel breadth. For a sufficiently large aspect ratio, there can be an interlude between these two periods during which the coefficient is nearly steady, signifying the resemblance of the transport to that in a parallel-plate channel. Given a sufficiently long time, the dispersion coefficient will reach a fully-developed steady value that may be several times higher than that with- out the side wall effects. The time scales for these periods of transience are identified in this paper.

Effect of electroosmotic flow on brine imbibition in porous media

Based on Darcy＇s Law and the Helmholta-Smoluchowski equation, an imbibition velocity formula for the water phase with an electric field was deduced, showing that the imbibition velocity with an electric field is to various extents not only related to the rock permeability and characteristic length, the fluid viscosity, the oil-water interface tension and the gravity of the imbibing brine, but also to the fluid dielectric permittivity, zeta potential, applied electric field direction, and strength. Imbibition experiments with electric fields that are different in direction and strength were conducted, showing that application of a positive electric field enhances the imbibition velocity and increases the imbibition recovery ratio, while application of a negative electric field reduces the imbibition velocity and decreases the imbibition recovery ratio. The imbibition recovery ratio with a positive electric field increases with the strength of the electric field, and the imbibition recovery ratio with a negative electric field is lower than that without an electric field.

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 PoissomBoltzmann equation, a hyperbolic par- tial 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 elas- ticity number and the angular Reynolds number increase due to the competition among the elastic, viscous, inertial, and electric forces in the flow.

Heat transfer analysis of MHD and electroosmotic flow of non-Newtonian fluid in a rotating microfluidic channel:an exact solution

The heat transfer of the combined magnetohydrodynamic(MHD)and electroosmotic flow(EOF)of non-Newtonian fluid in a rotating microchannel is analyzed.A couple stress fluid model is scrutinized to simulate the rheological characteristics of the fluid.The exact solution for the energy transport equation is achieved.Subsequently,this solution is utilized to obtain the flow velocity and volume flow rates within the flow domain under appropriate boundary conditions.The obtained analytical solution results are compared with the previous data in the literature,and good agreement is obtained.A detailed parametric study of the effects of several factors,e.g.,the rotational Reynolds number,the Joule heating parameter,the couple stress parameter,the Hartmann number,and the buoyancy parameter,on the flow velocities and temperature is explored.It is unveiled that the elevation in a couple stress parameter enhances the EOF velocity in the axial direction.

Talk about Several Time Periodic Pulse Electroosmotic Flow of Maxwell Fluid in a Circular Microchannel

Using the method of Laplace transform, analytical expressions are derived for the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid in circular microchannel. The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations of inverse Laplace transform, the effects of electrokinetic width K, relaxation time and pulse width a on the above several pulse EOF velocities are investigated. In addition, we focused on the comparison and analysis of the formulas and graphs between the triangle and sawtooth pulse EOF with the rectangle pulse EOF. The study found that there are obvious differences in formulas and graphs between triangle and sawtooth pulse EOF with rectangle pulse EOF, and the difference mainly depends on the different definitions of the three kinds of time periodic pulse waves. Finally, we also studied the stability of the above three kinds of pulse EOF and the influence of relaxation time on pulse EOF velocity under different pulse widths is discussed. We find that the rectangle pulse EOF is more stable than the triangle and sawtooth pulse EOF. For any pulse, as the pulse width a increases, the influence of the relaxation time on the pulse EOF velocity will be weakened.

Analytical Study of the Electroosmotic Flow of Two Immiscible Power-Law Fluids in a Microchannel

The multilayer microchannel flow is a promising tool in microchannel-based systems such as hybrid microfluidics. To assist in the efficient design of two-liquid pumping system, a two-fluid electroosmotic flow of immiscible power-law fluids through a microtube is studied with consideration of zeta potential difference near the two-liquid interface. The modified Cauchy momentum equation in cylindrical coordinate governing the two-liquid velocity distributions is solved where both peripheral and inner liquids are represented by power-law model. The two-fluid velocity distribution under the combined interaction of power-law rheological effect and circular wall effect is evaluated at different viscosities and different electroosmotic characters of inner and peripheral power-law fluids. The velocity of inner flow is a function of the viscosities, electric properties and electroosmotic characters of two power-law fluids, while the peripheral flow is majorly influenced by the viscosity, electric property and electroosmotic characters of peripheral fluid. Irrespective of the configuration manner of power-law fluids, the shear thinning fluid is more sensitive to the change of other parameters.

Rotating electroosmotic flows in soft parallel plate microchannels

We present a theoretical investigation of rotating electroosmotic flows(EOFs) in soft parallel plate microchannels. The soft microchannel, also called as the polyelectrolyte-grafted microchannel, is denoted as a rigid microchannel coated with a polyelectrolyte layer(PEL) on its surface. We compare the velocity in a soft microchannel with that in a rigid one for different rotating frequencies and find that the PEL has a trend to lower the velocities in both directions for a larger equivalent electrical double layer(EDL) thickness λFCL(λFCL = 0.3) and a smaller rotating frequency ω(ω < 5).However, for a larger rotating frequency ω(ω = 5), the main stream velocity u far away from the channel walls in a soft microchannel exceeds that in a rigid one. Inspired by the above results, we can control the EOF velocity in micro rotating systems by imparting PELs on the microchannel walls, which may be an interesting application in biomedical separation and chemical reaction.

Numerical Investigation of Traveling Wave Electroosmotic Flows in A Microchannel

In this paper, a coordinate transformation method (CTM) is employed to numerically solve the Poisson–Nernst–Planck (PNP) equation and Navier–Stokes (NS) equations for studying the traveling-wave electroosmotic flow (TWEF) in a two-dimensional microchannel. Numerical solutions indicate that the numerical solutions of TWEF with and without the coordinate transformation are in good agreement, while CTM effectively improves stability and convergence rate of the numerical solution, and saves computational cost. It is found that the averaged flow velocity of TWEF in a micro-channel strongly depends on frequency of the electric field. Flow rate achieves a maximum around the charge frequency of the electric double layer. The approximate solutions of TWEF with slip boundary conditions are also presented for comparison. It is shown that the NS solution with slip boundary conditions agree well with those of complete PNP-NS equations in the cases of small ratios of Electric double layer(EDL) thickness to channel depth(λD/H). The NS solution with slip boundary conditions over-estimates the electroosmotic flow velocity as this ratio(λD/H) is large.

Analytical study of pulsatile mixed electroosmotic and shear-driven flow in a microchannel with a slip-dependent zeta potential

The escalation of zeta potential by the influence of wall slip for the electrokinetically modulated flow through a microchannel motivates to consider the impact of hydrodynamic slippage upon the zeta or surface potential.The reported study undergoes an analytical exploration of the pulsatile electroosmosis and shear-actuated flow characteristics of a fluid with a Newtonian model through a microchannel with parallel plates by invoking the reliance of a zeta or surface potential on slippage.The linearized Poisson-Boltzmann and momentum equations are solved analytically to obtain the explicit expression of the electrical potential induced in the electrical double layer(EDL),the flow velocity field,and the volumetric flow rate for an extensive span of parameters.The velocity field proximal to the microchannel wall is observed to enhance by an apparent zeta potential,and is further escalated for a thinner EDL and an oscillating electric field with a higher amplitude.However,near the core region of the microchannel,the flow velocity becomes invariant with the EDL thickness.The result shows that the lower wall velocity contributes to the flow velocity along with the electroosmotic body force and the impact of the velocity of the wall underneath diminishes proximal to the upper wall.Moreover,the volumetric flow rate increases when the thickness of the EDL decreases,owing to the influence of the wall slip.However,for thinner EDLs and medium and higher oscillating Reynolds numbers,the volumetric flow rate varies non-monotonously,correlative to the slip-free and slip cases.

On Applicability of Poisson-Boltzmann Equation for Micro-and Nanoscale Electroosmotic Flows

The applicability of the Poisson-Boltzmann model for micro-and nanoscale electroosmotic flows is a very important theoretical and engineering problem.In this contribution we investigate this problem at two aspects:first the high ionic concentration effect on the Boltzmann distribution assumption in the diffusion layer is studied by comparisons with the molecular dynamics(MD)simulation results;then the electrical double layer(EDL)interaction effect caused by low ionic concentrations in small channels is discussed by comparing with the dynamic model described by the coupled Poisson-Nernst-Planck(PNP)and Navier-Stokes(NS)equations.The results show that the Poisson-Boltzmann(PB)model is applicable in a very wide range:(i)the PB model can still provide good predictions of the ions density profiles up to a very high ionic concentration(∼1 M)in the diffusion layer;(ii)the PB model predicts the net charge density accurately as long as the EDL thickness is smaller than the channel width and then overrates the net charge density profile as the EDL thickness increasing,and the predicted electric potential profile is still very accurate up to a very strong EDL interaction(λ/W∼10).

Lattice Poisson-Boltzmann Simulations of Electroosmotic Flows in Charged Anisotropic Porous Media

This paper presents numerical analysis of electroosmotic flows(EOF)in charged anisotropic porous media using the lattice Poisson-Boltzmann method(LPBM),which combines two sets of lattice evolution methods solving the nonlinear Poisson equation for electric potential distribution and the Navier-Stokes equations for fluid flow respectively.Consistent boundary condition implementations are proposed for solving both the electrodynamics and the hydrodynamics on a same grid set.The anisotropic structure effects on EOF characteristics are therefore studied by modeling the electrically driven flows through ellipse arrays packed in a microchannel whose shape and orientation angle are used to control the anisotropy of porous media.The results show that flow rates increase with the axis length along the external electric field direction for a certain porosity and decrease with the angle between the semimajor axis and the bulk flow direction when the orientation angle is smaller thanπ/2.After introducing random factors into the microstructures of porous media,the statistical results of flow rate show that the anisotropy of microstructure decreases the permeability of EOFs in porous media.

A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces

We develop a continuum hydrodynamic model for two-phase immiscible flows that involve electroosmotic effect in an electrolyte and moving contact line at solid surfaces.The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation.This approach was first presented in the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows(Qian,Wang,and Sheng,J.Fluid Mech.564,333-360(2006)).Physically,the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime.Therefore,the same variational approach is applied here to the derivation of the continuum hydrodynamic model for charged two-phase immiscible flows where one fluid component is an electrolyte exhibiting electroosmotic effect on a charged surface.A phase field is employed to model the diffuse interface between two immiscible fluid components,one being the electrolyte and the other a nonconductive fluid,both allowed to slip at solid surfaces.Our model consists of the incompressible Navier-Stokes equation for momentum transport,the Nernst-Planck equation for ion transport,the Cahn-Hilliard phase-field equation for interface motion,and the Poisson equation for electric potential,along with all the necessary boundary conditions.In particular,all the dynamic boundary conditions at solid surfaces,including the generalized Navier boundary condition for slip,are derived together with the equations of motion in the bulk region.Numerical examples in two-dimensional space,which involve overlapped electric double layer fields,have been presented to demonstrate the validity and applicability of the model,and a few salient features of the two-phase immiscible electroosmotic flows at solid surface.The wall slip in the vicinity ofmoving contact line and the Smoluchowski slip in the electric double layer are both investigated.

Numerical simulation of electroosmotic flow in hydrophobic microchannels

Electroosmotic flow(EOF) is a promising way for driving and mixing fluids in microfluidics.For the parallel-plate microchannel with the hydrophobic surface, this paper solved the governing equations using the finite element method(FEM), and the effects of microchannel height, electric strength and ionic concentration on EOF were thus investigated.The simulation indicates that the transient characteristics of EOF are similar in hydrophobic and hydrophilic microchannels, the steady time of EOF is proportional to the square of microchannel height, and the scale is microsecond.EOF velocity is proportional to the electric strength and independent of the channel height, and decreases slowly with the ionic concentration, which is lower than that in hydrophilic microchannel due to the presence of slip length in hydrophobic microchannel.The results can provide valuable insights into the optimal design of microchannel surfaces to achieve accurate EOF control in hydrophobic microchannel.

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel

This paper investigates the magnetohydrodynamic(MHD) electroosmotic flow(EOF) of Newtonian fluid through a zeta potential modulated parallel plate microchannel with patterned hydrodynamic slippage. The driven mechanism of the flow originates from the Lorentz force generated by the interaction of externally imposed lateral electric field Ey and vertical magnetic field Bz and electric field force produced by an externally applied electric field Ex. It is assumed that the wall zeta potential and the slip length are periodic functions of axial coordinate x, an analytical solution of the stream function is achieved by utilizing the method of separation of variables and perturbation expansion. The pictures of streamlines are plotted and the vortex configurations produced in flow field due to patterned wall potential and hydrodynamic slippage are discussed. Based on the stream function, the velocity field and volume flow rate are obtained, which are greatly depend on some dimensionless parameters, such as slip length ls, electrokinetic widthλ, the amplitude δ of the patterned slip length, the amplitude m of the modulated zeta potential and Hartmann number Ha. The variations of velocity and volume flow rate with these dimensionless parameters are discussed in details. These theoretical results may provide some guidance effectively operating micropump in practical nanofluidic applications.