Joule heating effect of electroosmosis in a finite-length microchannel made of different materials

This paper presents a numerical analysis of Joule heating effect of electroosmo- sis in a finite-length microchannel made of the glass and polydimethylsiloxane （PDMS） polymer. The Poisson-Boltzmann equation of electric double layer, the Navier-Stokes equation of liquid flow, and the liquid-solid coupled heat transfer equation are solved to investigate temperature behaviors of electroosmosis in a two-dimensional microchannel. The feedback effect of temperature variation on liquid properties （dielectric constant, vis- cosity, and thermal and electric conductivities） is taken into account. Numerical results indicate that there exists a heat developing length near the channel inlet where the flow velocity, temperature, pressure, and electric field rapidly vary and then approach to a steady state after the heat developing length, which may occupy a considerable portion of the microchannel in cases of thick chip and high electric field. The liquid temperature of steady state increases with the increase of the applied electric field, channel width, and chip thickness. The temperature on a PDMS wall is higher than that on a glass wall due to the difference of heat conductivities of materials. Temperature variations are found in the both longitudinal and transverse directions of the microchannel. The increase of the temperature on the wall decreases the charge density of the electric double layer. The longitudinal temperature variation induces a pressure gradient and changes the behavior of the electric field in the microchannel. The inflow liquid temperature does not change the liquid temperature of steady state and the heat developing length.     

Periodical streaming potential and electro-viscous effects in microchannel flow

This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.     

Periodical streaming potential and electro-viscous effects in microchannel flow

This paper presents an analytical solution to periodical streaming potential,flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson.Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow.Dimensional analysis indicates that electric-Viscous force depends on three factors:(1)Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state,(2)profile function describing the distribution profile of electro-viscous forcein channel section,and(3)coupling coefficient reflecting behavior of amplitude damping and phase Offset of electro-viscous force.Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number(Re=wh2/v).Flow-induced electric field varies very slowly with Re when Re＜1.and rapidly decreases when Re＞1.Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.     

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer(EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.     

动电学效应下微流动近壁面带电离子受力分析

应用离子分布的Boltzmann定律和Poisson方程研究了微流动中通道近壁面电势的分布,采用Derjaguin理论计算了动电学效应下带电离子受到的双电层作用力,应用Hamaker-De Boer 近似式得到了离子与壁面间的范德瓦尔力,同时也考虑到离子重力的影响,揭示了三种力对带电离子流动特性的影响.研究结果表明:无量纲间距d~*≤0.2时,离子重力的影响可以忽略,带电离子主要受范德瓦尔力和双电层作用力的作用,且二力均随d~*增大而减小,d~*≤0.02时,范德瓦尔力起主要作用,当0.020.2时,重力、范德瓦尔力及双电层作用力都趋于零,均可忽略.     

生物芯片中周期性电渗驱动液体薄膜的流动特性

研究了二维周期性电渗驱动液体薄膜的流动特性. 以Debye-Hückel 假设近似下线性化的Poisson-Boltzmann方程描述双电层电动势分布和电荷密度的分布关系, 与黏性不可压缩流体Navier-Stokes方程相耦合, 得到流体在自由面与固壁之间的周期电渗流流场的精确解. 结果显示, 薄膜内速度振幅与流体黏性密切相关, 雷诺数越大, 速度振幅就越小. 该文还细致分析了雷诺数和自由面ζ电势对自由面的流速振幅和薄膜内速度相位差的影响.     

Thickness-averaged model for numerical simulation of electroosmotic flow in three-dimensional microfluidic chips

The microfluidic system is a multi-physics interaction field that has attracted great attention. The electric double layers and electroosmosis are important flow-electricity interaction phenomena. This paper presents a thickness-averaged model to solve three-dimensional complex electroosmotic flows in a wide-shallow microchannel/chamber combined (MCC) chip based on the Navier-Stokes equations for the flow field and the Poisson equation to the electric field. Behaviors of the electroosmotic flow, the electric field, and the pressure are analyzed. The quantitative effects of the wall charge density (or the zeta potential) and the applied electric field on the electroosmotic flow rate are investigated. The two-dimensional thickness-averaged flow model greatly simplifies the three-dimensional computation of the complex electroosmotic flows, and correctly reflects the electrookinetic effects of the wall charge on the flow. The numerical results indicate that the electroosmotic flow rate of the thickness-averaged model agrees well with that of the three-dimensional slip-boundary flow model. The flow streamlines and pressure distribution of these two models are in qualitative agreement.     

生物芯片微通道周期性电渗流特性

以双电层的Poisson-Boltzmann方程和黏性不可压缩流体运动的Navier-Stokes方程为 基础,提出二维均匀微通道周期电渗流的解析解. 分析结果表明,周期电渗流速度大 小不但与双电层特性和外电场有关, 而且与流动雷诺数(Re = \omega h^2/\nu )密切相关. 随雷诺数增加,双电层滑移速度下降. 当离开固壁距离增加时,双电层以外区域流动速度快 速衰减,速度滞后相位角明显增加. 研究发现在微通道有波浪状速度剖面. 给出在低雷 诺数时的周期电渗流渐近解,它的速度振幅与定常电渗流速度相同,并具有柱栓式速度分布 形态. 还得到在微通道宽对双电层厚的比值(\kappa h)很小时,Debye-H\"{u}ckel近似 的周期电渗流解, 并与解析解进行分析比较 微通道,双电层,周期电渗流,雷诺数     

A coordinate transformation method for numerical solutions of the electric double layer and electroosmotic flows in a microchannel

The electric double layer (EDL) and electroosmotic flows (EOFs) constitute the theoretical foundations of microfluidics. Numerical solution is one of the effective means of analysis in microfluidics. In general, it is difficult to obtain an accurate numerical solution of complex EOFs because of multiphysical interactions and locally high gradients. In this paper, a new coordinate transformation method is proposed to numerically solve the Poisson–Boltzmann, Navier–Stokes and Nernst–Planck equations to study the EDL and complex EOFs in a microchannel. A series of numerical examples is presented including cases of a homogeneous, discontinous wall electric potential and a locally high wall potential. A systematic comparison of numerical solutions with and without the coordinate transformation is carried out. The numerical results indicate that the coordinate transformation effectively decreases the gradient of the electric potential, ion concentration and electroosmotic velocity in the vicinity of the solid wall, and greatly improves the stability and convergency of the solution. In a transformed coordinate system with a coarse grid, the numerical solutions can be as accurate as those in the original coordinate system with a refined grid. Copyright © 2011 John Wiley & Sons, Ltd.     

坐标变换法数值求解微通道行波电场电渗流

采用坐标变换法数值求解了耦合的Poisson-Nernst-Planck (PNP)方程和Navier-Stokes(NS)方程, 研究二维狭窄微通道行波电场电渗流数值解. 数值结果表明,坐标变换法能有效降低电渗流解数值解在双电层的高梯度, 有效改善数值解的收敛性和稳定性. 坐标变换的电渗流数值解和原始坐标下的数值解完全一致. 坐标变换后采用简单的网格也能得到和原始坐标下复杂网格相同的解. 给出了滑移边界的近似解与完整的PNP-NS数值解的比较. 在双电层厚度与微通道深度比值(λ/H)很小的情况下(相对深通道), 两者的解基本一致. 但在λ/H较大时(相对浅通道)滑移边界的解高于电渗流速度.      

Flow behavior in microchannel made of different materials with wall slip velocity and electro-viscous effects

In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressuredriven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the fow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large kh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.     

薄膜润滑中双电层效应的理论分析与实验研究

建立了考虑双电层效应的有限宽组合滑块薄膜润滑数学模型,并利用组合滑块与圆盘的滑动摩擦试验对双电层效应进行研究,利用实验结果修正了润滑过程中双电层效应的计算,给出电粘度的计算公式并进行数值分析.结果表明:在薄膜厚度较薄的情况下,双电层效应使得流体的等效粘度随膜厚减小而迅速增加;随着膜厚增加,双电层的电粘度效应逐渐减弱;随着电场强度增加,双电层的电粘度效应增加,当电场强度达到一定程度时,双电层的电粘度效应开始减弱.     

Alterations in peristaltic pumping of Jeffery nanoliquids with electric and magnetic fields

The combined effects of electric and magnetic fields on peristaltic flow of Jeffery nanoliquids are analytically investigated. Double-diffusive convection in the asymmetric microchannel is also carried out. The walls of the microchannel are propagating with a finite phase difference in a sinusoidal manner. Rosseland diffusion flux model is employed to examine the thermal radiation effect. The zeta potential on the walls is considered very low to apply Hückel–Debye approximations. The coupled non-linear governing equations are simplified by using dimensional analysis and lubrication theory. The closed form solutions for potential function, nanoparticle fraction field, solute concentration field, temperature field, stream function, and axial velocity are derived under the appropriate boundary conditions. It is noteworthy that the pumping characteristics strongly depend on the magnetic fields, electric fields, electric double layer thickness, Jeffery parameter, thermal radiation and Grashof number. Furthermore, trapping phenomenon is analyzed under the effects of Hartmann number, Jeffrey parameter, Grashof number and Helmholtz–Smoluchowski velocity. The novelty of the present work is the amalgamation of biomimetics (peristaltic propulsion), electro-magneto-hydrodynamics and nanofluid dynamics to produce a smart pump system model for smart drug delivery systems.     

Electrical classification of single red blood cell deformability in high-shear microchannel flows

A sensor that can efficiently and sequentially measure the deformability of individual red blood cell (RBC) flowing along a microchannel is described. Counter-electrode-type microsensors are attached to the channel bottom wall, and as RBCs pass between the electrodes, the time series of the electric resistance is measured. An RBC is deformed by the high shear flow to a degree dependent upon its elastic modulus. Hence, the profile of the resistance, which is unique to the shape of the RBC, can be analyzed to obtain the deformability of each cell. First, theoretical and experimental analyses were conducted to identify the specific AC frequency at which the effect of the electric double layer formed on the electrode surface is minimized. Measurements were then conducted upon samples of normal human RBCs and glutaraldehyde-treated (rigidified) RBCs to evaluate the feasibility of the present method. In addition, simultaneous visualization of RBC deformation was performed using a high-speed camera. Normal RBCs were observed to have a degree of deformation index (DI) of around 0.57, whereas the rigidified RBCs was DI = 0 in the microchannel. The experimental measurements showed a strong correlation between the half-width of the maximum of the resistance distribution and the DI of the RBC.     

Microbubble lensing-induced photobleaching (μ-BLIP) with application to microflow visualization

The curvature of gas–liquid interfaces and the step change in properties across these interfaces in microchannels are shown here to create a powerful lens/mirror effect. In a hydrophilic system, light incident on the bubble is focused into the surrounding liquid, resulting in a locally increased total light exposure. The optical phenomena leading to this are discussed, and the effect is demonstrated experimentally by imaging the increased photobleaching rate of fluorophores in the near-bubble region. Numerical simulations of the system are performed to investigate the electrical potential and flow fields resulting from the application of an axial electric field. Microbubble lensing-induced photobleaching (-BLIP) is then applied as a method to inject a negative scalar flow marker for flow visualization in microchannels. Once formed, the electrokinetic transport of this marker is analyzed to determine the cross-channel velocity profile of the liquid phase and the liquid velocity in the film. Experimental data is verified by comparison with numerical predictions and previous experimental studies. This contribution represents both a new application of microscale gas–liquid interfacial phenomena, and a new technique for microfluidic flow visualization, particularly applicable (though not limited) to the study of multiphase microchannel flows.     

Layered model of electrorheological fluid under flow

We present a theoretical model of the behavior of a concentrated electrorheological fluid (ERF) which explicitly takes into account the effects of conductivity. The increase in shear viscosity under an electric field is due to a layered structure between the electrodes, made up of the remnants of particle chains adhering to the electrodes by electrostatic image forces, and a freely flowing liquid layer where all the shear flow is concentrated. This layered model can explain the variation of electric current with shear rate, as well as the rheological response of a dynamic yield stress proportional to the square of the applied electric field.     

Quantitative measurement of depth–averaged concentration fields in microchannels by means of a fluorescence intensity method

We have inferred and verified an optical measuring technique, based on fluorescence intensity, for the species concentration field in a liquid microchannel flow. In contrast to macroscopic flows, where a light sheet is usually applied, the complete illumination of the measuring volume in the microchannel provides a height-averaged concentration field. The technique was verified with aqueous solutions within a square glass microchannel of 110 μm width. The verification experiments confirm both a good spatial resolution and a good accuracy of even the concentration gradients within a concentration boundary layer.     

Electric fields in the rheology of disperse systems

In the present survey, the influence of electric fields on the structure and rheological properties of disperse systems as well as the effect of deformations on their electrical characteristics are discussed. The properties of these systems are considered in terms of the dielectric permittivity and electrification potential. The considerable thickness of the double electric layer around the disperse phase particles, which is characteristic of disperse systems with nonpolar hydrocarbon dispersion media, provides the possibility for strong electric fields to produce an electric nonuniformity on the surface of the disperse phase particles. The formation of hydrate layers on the particles creates the possibility of polarization of the disperse phase. In plastic disperse systems such as greases, a strong orientation effect is observed, which contributes to the creation of frozen flow patterns when the flow is suddenly stopped. The survey is concluded with a consideration of the process of formation of chain structures in the direction of the lines of force of the electric field whose orientation is normal to the direction of flow, which can lead to complete stoppage of the flow.     

Double layer overlap in ac electroosmosis

The frequency-dependent flow of electrolytes between pairs of parallel plate micro-electrodes is analyzed in this paper, for the cases in which electric double layers formed in vicinity of the solid boundaries may strongly interact with each other. Closed form expressions for the potential distributions are first developed under certain simplifying assumptions, depicting the interactions between the oscillating electric field and charge density distribution within the double layer. It is revealed that the impact of double layer overlap on ac electroosmotic flows turns out to be more predominant at frequencies of the order of relaxation frequency of the electrode–electrolyte system. At higher frequencies, potential drop across the double layer tends to zero, due to polarization of the electrode-solution interface, and virtually no electroosmotic flows can be obtained in such cases.     

Electroviscous effects in steady fully developed flow of a power-law liquid through a cylindrical microchannel

Electroviscous effects in steady, fully developed, pressure-driven flow of power-law liquids through a uniform cylindrical microchannel have been investigated numerically by solving the Poisson–Boltzmann and the momentum equations using a finite difference method. The pipe wall is considered to have uniform surface charge density and the liquid is assumed to be a symmetric 1:1 electrolyte solution. Electroviscous resistance reduces the velocity adjacent to the wall, relative to the velocity on the axis. The effect is shown to be greater when the liquid is shear-thinning, and less when it is shear-thickening, than it is for Newtonian flow. For overlapping electrical double layers and elevated surface charge density, the electroviscous reduction in the near-wall velocity can form an almost stationary (zero shear) layer there when the liquid is shear-thinning. In that case, the liquid behaves approximately as if it is flowing through a channel of reduced diameter. The induced axial electrical field shows only a weak dependence on the power-law index with the dependence being greatest for shear-thinning liquids. This field exhibits a local maximum as surface charge density increases from zero, even though the corresponding electrokinetic resistance increases monotonically. The magnitude of the electroviscous effect on the apparent viscosity, as measured by the ratio of the apparent and physical consistency indices, decreases monotonically as the power-law index increases. Thus, overall, the electroviscous effect is stronger in shear-thinning, and weaker in shear-thickening liquids, than it is when the liquid is Newtonian.