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.

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.

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.

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.

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.

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.

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.

赤道太平洋温度、流场距平EOF分析及与厄尔尼诺的关系

利用EOF分析方法,讨论了最近20a赤道太平洋次表层温度、纬向流距平与厄尔尼诺的关系.结果表明:赤道太平洋海温距平EOF分析第一、二主分量占总量的近80％,其中第一主分量类似于厄尔尼诺模态,第二主分量类似于暖池模态;后一模态存在着突变和渐变两种过程,其中由冷位相变暖位相过程为渐变过程,而暖位相变冷位相过程为突变过程.厄尔尼诺事件是赤道西太平洋暖池突变过程的结果.赤道太平洋纬向流距平EOF的第二主分量代表赤道西太平洋潜流和东太平洋南赤道流的变化,这个模态存在着半年左右的振荡和与厄尔尼诺同位相的年际振荡两种频率.另外,它还存在明显的年代际变化.赤道西太平洋潜流和东太平洋南赤道流减弱是产生厄尔尼诺的必要条件.统计回归分析表明,赤道太平洋海温距平和纬向流距平EOF的第二特征向量的时间系数对厄尔尼诺和拉尼娜均有一定的预报意义.

微通道中一类生物流体在高Zeta势下的电渗流及传热特性

在高壁面Zeta势下,研究滑移边界条件下满足牛顿流体模型的一类生物流体的电渗流动及传热特性,流体在外加电场、磁场和焦耳加热共同作用下流动.首先,在不使用Debye-Hückel线性近似条件时,利用切比雪夫谱方法给出非线性Poisson-Boltzmann方程和流函数满足的四阶微分方程及热能方程的数值解,将所得结果与利用Debye-Hückel线性近似所得结果进行比较,证明本文数值方法的有效性.其次,讨论电磁环境下壁面Zeta势、哈特曼数H、电渗参数m、滑移参数β对流动特性、泵送特性和捕获现象的影响,并探究焦耳加热参数γ和布林克曼数Br等参数对传热特性的影响.结果表明,壁面Zeta势、电渗参数m、滑移参数β的增大对流体速度有促进作用,而哈特曼数H的增大会抵抗流体流动.研究进一步表明,焦耳加热参数γ和布林克曼数Br的增大会导致温度升高.

平行板微通道中一类不可压缩微极性流体在高Zeta势下的时间周期电渗流

在高Zeta势下,研究平行板微通道中一类不可压缩微极性流体的时间周期电渗流.在不使用DebyeHüickel线性近似条件下,利用有限差分法数值求解非线性Poisson-Boltzmann方程和不可压缩微极性流体的连续性方程、动量方程、角动量方程及本构方程,在低Zeta势下将所得结果与使用Debye-Hückel线性近似得到的解析解比较,证明本文数值方法是可行的;讨论高Zeta势下电动宽度m、电振荡频率Ω、微极性参数k1等无量纲参数对不可压缩微极性流体的速度和微旋转效应的影响.研究表明:1)随着Zeta势的增大,微极性流体的速度、微旋转、体积流量、微旋强度以及剪切应力增大,说明与低Zeta势相比,高Zeta势对微极性流体电渗流有显著的促进作用.2)在高Zeta势下,随着微极性参数的增大,微极性流体的速度减小,但是对微旋转效应呈现先增强后减弱的趋势.3)在高Zeta势下,当电振荡频率较低(小于1)时,电动宽度的增大促进微极性流体的流动,但抑制其微旋转;当电振荡频率较高(大于1)时,电动宽度的增大抑制微极性流体的流动及微旋转,但促进体积流量快速增大并趋于恒定.4)在高Zeta势下,当电振荡频率较低(小于1)时,微极性流体电渗流速度和微旋转随着电振荡频率的变化呈现明显的振荡变化趋势,但是速度和微旋转的峰值、体积流量及微旋强度均保持不变;当电振荡频率较高(大于1)时,随着电振荡频率的增大,微极性流体电渗流速度和微旋转的幅值减小,体积流量及微旋强度减小直至趋于零.5)在高Zeta势下,壁面剪切应力σ21及σ12的幅值随电动宽度的增大而增大;当电振荡频率较低(小于1)时,壁面剪切应力σ21与σ12不随电振荡频率的增大而变化,均取恒定值,且微极性参数的取值不影响壁面剪切应力σ21的幅值;当电振荡频率较高(大于1)时,壁面剪切应力σ21及σ12的幅值随电振荡频率的增大而减小,且壁面剪切应力σ21的幅值随着微极性参数的增大而减小,而壁面剪切应力σ12的振幅随着微极性参数的增大而线性减小.

珠江三角洲典型灰霾天气过程和清洁过程近地层流场的EOF对比分析

利用广东省466个地面自动气象站资料、广州气象站常规气象资料及珠江三角洲4个主要城市的PM10浓度等资料，通过矢量EOF方法，对选出的珠江三角洲典型灰霾天气过程（2004年1月4～10日）和清洁过程（2005年11月15～21日）的近地层流场进行对比分析。分析表明典型灰霾天气过程第二、三模态有非常明显的日变化特征，受局地中小尺度环流系统影响，污染物局限在当地，出现严重的灰霾天气；而清洁过程与强平流输送有关，主要受大尺度环流系统影响。

蒙脱土中镧、钇离子电迁移行为试验研究

为研究蒙脱土对轻稀土离子La^(3+)和重稀土离子Y^(3+)吸附的差异,及外加电场条件下两种离子在蒙脱土中的迁移规律,开展了不同条件下的等温吸附试验、稀土迁移和电渗试验等.研究结果表明,Langmuir等温吸附方程对La^(3+)和Y^(3+)在蒙脱土表面的吸附拟合度较高,与La^(3+)吸附相比,蒙脱土对Y^(3+)的饱和吸附量更高.而在电渗试验中,蒙脱土吸附的La^(3+)和Y^(3+)含量远小于等温吸附试验中所得到饱和吸附量,表明电渗过程中吸附和电迁移是一个相互耦合的过程,且电势梯度为1 V/cm时更利于稀土在蒙脱土中的迁移.此外,基于试验中La^(3+)和Y^(3+)迁移的距离、迁移的电荷占比和迁移所消耗的电能三个因素,分析离子了镧、钇的迁移效率,发现La^(3+)在蒙脱土中的迁移效率高于Y^(3+).试验结果可为稀土矿清洁开采相关研究提供参考.