T型微混合器内混合强化的数值模拟

为了研究不同混合强化方式对微混合的影响,采用有限元法对T型微混合器内增加壁面非均匀Zeta电势的主动式混合以及嵌入肋板的被动式混合进行了数值模拟.对比分析了3种T型微混合器内流场、速度场和浓度场的分布,并研究了不同T型微混合器内溶液混合效率与Re和Sc之间的关系.研究结果表明,两种溶液的混合效率随着Re和Sc的增加非线性减小,且减小趋势变缓;嵌入肋板的被动式T型微混合器内的混合效率沿水平微通道方向上存在较大的波动;增加壁面非均匀Zeta电势的主动式T型微混合器内的混合效率沿水平微通道方向上的波动较小,且这种波动在高Re或低Sc时会被抑制.Re对混合方式的强化效果也有很大的影响.当Re较小时,增加壁面非均匀Zeta电势的主动式混合能更好地提高溶液的混合效率,但当Re较大时,嵌入肋板的被动式混合的混合效果更好.     

高zeta势下Phan-Thien-Tanner(PTT)流体的电渗微推进器北大核心CSCD

在高的壁面zeta电势下,考查了Phan-Thien-Tanner(PTT)黏弹性流体在平行板微通道中的电渗推进器问题.在没有考虑Debye-Hückel线性近似的条件下,求解了非线性Poisson-Boltzmann方程,得到了高zeta电势下电势的解析解.通过求解PTT流体满足的Cauchy动量方程,获得了Navier滑移条件下微推进器速度的数值解.进而通过数值积分得到了电渗微推进器的性能分布,包括比冲、推力、效率和推力-功率比.最后,详细分析了黏弹性参数、壁面zeta电势、滑移系数和双电层厚度对速度分布及推进器性能的影响.结果表明,与Newton流体相比,PTT流体作为推进剂有利于推进器性能的提高,比如,流体速度随着黏弹性参数的增大而增大,导致推进器性能也呈增大的趋势.此外,当前推进器比冲为800~1000 ms时,推力可达0~250μN,效率为6%~12%,推力-功率比为0~20 mN/W.     

微通道内电渗压力混合驱动幂律流体流动模拟

为了研究微通道内电渗压力混合驱动幂律流体的流动特性,建立了微通道内电渗压力混合驱动幂律流体的计算模型,其双电层电势、流体的流场分布分别由Poisson-Boltzmann(P-B)方程和Navier-Stokes(N-S)方程描述.讨论了无量纲Debye(德拜)参数K、壁面ζ*电势和幂律指数n对流体流动特性和Poiseuille数的影响.结果表明,当压力梯度与外加电场方向一致(Γ0)时,剪切变稀流体的速度大于剪切变稠流体;压力梯度与外加电场方向相反(Γ0)时,结果相反.Poiseuille数是无量纲Debye常数K、壁面ζ*电势和幂律指数n的增函数.     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

周期壁面电势调制下平行板微管道中的电磁电渗流动

研究了平行板微管道中二维磁流体(MHD)电渗流(EOF)在zeta电势调制下的流动.流体的流动是由两个外加水平电场和垂直磁场所产生的Lorentz力和电场力的组合驱动的.在滑移边界条件下,得到了流函数以及速度分布的解析解.详细讨论了速度随Hartmann数Ha、滑移长度B、电动宽度K等相关的无量纲参数量级变化的变化规律.结果表明,调制的壁面电势会产生一个垂直速度分量,从而导致涡旋的形成.此外,可以观察到,速度的大小随着滑移长度B和电动宽度K的增大而增大.值得注意的是,速度的大小随着Ha值的增大而减小,这与一维流动中Ha值存在临界值的情况不同.     

异质材料有限长微通道电渗流热效应

采用数值方法,分析有限长PDMS/玻璃微通道电渗流热效应．数值求解双电层的Poisson-Boltzmann方程,液体流动的Navier-Stokes方程和流-固耦合的热输运方程,分析二维微通道电渗流的温度特性．考虑温度变化对流体特性（介电系数、粘度、热和电传导率）的反馈效应．数值结果表明,在通道进口附近有一段热发展长度,这里的流动速度、温度、压强和电场快速变化,然后趋向到一个稳定状态．在高电场和厚芯片的情况下,热发展长度可以占据相当一部分的微通道．电渗流稳定态温度随外加电场和芯片厚度的增加而升高．由于壁面材料的热特性差异,在稳定态时的PDMS壁面温度比玻璃壁面温度高．研究还发现在微通道的纵向和横向截面有温度变化．壁面温升降低双电层电荷密度．微通道纵向温度变化诱发流体压强梯度和改变微通道电场特性．微通道进流温度不改变热稳定态的温度和热发展长度．     

矩形纳米管道中的电动能量转换效率

利用分离变量法,研究了矩形纳米管道内流体的流向势及电动能量转换效率.通过求解电势满足的Poisson-Boltzmann(泊松-玻尔兹曼)方程和速度满足的Navier-Stokes(纳维-斯托克斯)方程,得到了矩形纳米管道内流体的流向势和电动能量转换效率的解析表达式.通过数值计算,分析了电动宽度K(矩形管道的宽度与双电层厚度的比值)、纳米管道高度与宽度的展向比α以及壁面Zeta势ζ等无量纲参数对流向势及电动能量转换效率的影响.结果表明,当其他参数固定时,流向势随K的增加而减小.当K较小时,电动能量转换效率随K的增大而增大;当K较大时,电动能量转换效率随K的增大而减小.此外,流向势随展向比α的增大而变大.对于较小的K,电动能量转换效率随α的增大而变大;当K较大时,电动能量转换效率随α增大而减小.最后,当壁面电势ζ增大,流向势变大,相应的电动能量转换效率有显著的增加.     

微通道液体流动双电层阻力效应

采用数值方法求解双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程,研究微通道双电层对压强梯度液体流动的阻力效应． 量纲分析表明,双电层阻力大小可以用一个无量纲的电阻力数表示．它与液体的介电系数、固体表面的zeta电位平方成正比,与液体的动力粘性系数、电导率以及微通道的宽度平方成反比．在计算流动诱导的流动电位势和电阻力时,提出电流密度平衡条件,可以消除传统电流平衡条件导致的固壁附近产生局部回流的不合理物理现象．还给出不同电阻力数的微通道流量、流量损失率、速度剖面的数值结果,合理解释了双电层对微通道液体流动的阻力效应．     

基于修正偶应力理论的Timoshenko微梁模型和尺寸效应研究

基于修正偶应力理论,将Timoshenko微梁的应力、偶应力、应变、曲率等基本变量,描述为位移分量偏导数的表达式.根据最小势能原理,推导了决定Timoshenko微梁位移场的位移场控微分方程.利用级数法求解了任意载荷作用下Timoshenko简支微梁的位移场控微分方程,得到了反映尺寸效应的挠度、转角及应力的偶应力理论解.通过对承受余弦分布载荷Timoshenko简支微梁的数值计算,研究了Timoshenko微梁的挠度、转角和应力的尺寸效应,分析了Poisson比对Timoshenko微梁力学行为及其尺寸效应的影响.结果表明:当截面高度与材料特征长度的比值小于5时,Timoshenko微梁的刚度和强度均随着截面高度的减小而显著提高,表现出明显的尺寸效应;当截面高度与材料特征长度的比值大于10时,Timoshenko微梁的刚度与强度均趋于稳定,尺寸效应可以忽略;材料Poisson比是影响Timoshenko微梁力学行为及尺寸效应的重要因素,Poisson比越大Timoshenko微梁刚度和强度的尺寸效应越显著.该文建立的Timoshenko微梁模型,能有效描述Timoshenko微梁的力学行为及尺寸效应,可为微电子机械系统（MEMS）中的微结构设计与分析提供理论基础和技术参考.     

中低纬电离层电场理论模式

介绍了一个电离层电场理论模式. 该模式从电离层发电机理论的基本方程出发, 采用地磁偶极坐标系, 推导出电离层电势满足的微分方程作为电场理论模式的出发方程. 模式的主要输入参量为电离层背景中性风(由经验模式HWM93给出)和电导率(由经验模式IRI90, MSISE90分别给出的电子和离子的浓度、温度以及中性大气的浓度、温度计算得出). 采用松弛迭代法求解电势的偏微分方程得出电势, 进而获得中低纬电离层电场、电流随时间、高度和地磁纬度的分布. 模式很好地再现了电离层电势、电场和赤道电急流的基本结构和形态, 可应用于对高层大气和电离层的电动力学过程的研究.     

Effect of temperature-dependent properties on electroosmotic mobility at arbitrary zeta potentials

A theoretical analysis to determine the electroosmotic mobility in an electroosmotic flow (EOF) in a microchannel at arbitrary zeta potentials is conducted in this study. As an important characteristic in this work, we consider that the wall zeta potentials of the microchannel and the viscosity and electrical conductivity of the electrolyte solution vary with temperature. The flow and the electric and temperature fields are obtained using lubrication approximation theory (LAT) together with the application of the regular perturbation technique. The electroosmotic mobility is evaluated, showing an increase higher than 18% (for the values of the physical properties used in this work) when physical properties, including the zeta potential of the microchannel walls, are considered as temperature-dependent functions compared with the isothermal case. Additionally, we show that the volumetric flow rate is drastically influenced when the zeta potential varies with temperature.     

Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

We present a coupled lattice Boltzmann method (LBM) to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst–Planck equation for the ion concentration, and the Navier–Stokes equation for the flows of the electrolyte solution. In the proposed LBM, the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator, which maintains the locality of the algorithm inherent to the original LBM. Furthermore, the Neumann-type boundary condition at the solid/liquid interface is then correctly imposed. In order to validate the present LBM, we consider an electro-osmotic flow in a slit between two charged infinite parallel plates, and the results of LBM computation are compared to the analytical solutions. Good agreement is obtained in the parameter range considered herein, including the case in which the nonlinearity of the Poisson equation due to the large potential variation manifests itself. We also apply the method to a two-dimensional problem of a finite-length microchannel with an entry and an exit. The steady state, as well as the transient behavior, of the electro-osmotic flow induced in the microchannel is investigated. It is shown that, although no external pressure difference is imposed, the presence of the entry and exit results in the occurrence of the local pressure gradient that causes a flow resistance reducing the magnitude of the electro-osmotic flow.     

A hybrid model for electroosmotic flows in microchannels induced by internal electrodes

Internal electrodes, adjacent to insulating walls at defined zeta potential, lead to a non-continuous potential distribution at the wall. Hence, simplified treatment appears problematic due to the singularity of the electrical field strength. To avoid this difficulty, we develop a hybrid model, which solves the electrical problem, including a resolution of the EDL, while the flow problem is solved in the fluid bulk only. We apply this hybrid model to investigate the position of internal electrodes with regard to their influence onto the flow field, driven by electroosmosis in a modular rectangular microchannel. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electroosmotic flow and heat transfer in a heterogeneous circular microchannel

Asymmetries in boundary condition are inevitable in practice in microfluidic channels, despite being rarely addressed from theoretical perspectives. Here, by arriving at closed form analytical solutions, we bring out a unique coupling between asymmetries in surface charge and heat transfer in electroosmotically driven microchannel flows. For illustration, we assume that the channel is laterally composed of two parts, each having specified values of the zeta potential and the wall heat flux. Considering low zeta potentials, we obtain analytical solutions in terms of infinite series for the dimensionless forms of the electric potential, the velocity, and the temperature distributions. We demonstrate that, by carefully adjusting the governing parameters, a variety of flow patterns may be achieved, a property that is crucial in applications such as liquid-phase transportation and mixing. Moreover, we show that the average velocity is a linear function of both the zeta potential ratio and the coverage factor. We further show that the average Nusselt number increases when part of the channel having the larger heat flux enlarges and the zeta potential of the part having the smaller surface charge increases. Hence, the maximum heat transfer rates are achieved when the boundary conditions are symmetrical.     

Micromixing effects on the dynamic behavior of continuous free-radical solution polymerization tank reactors

The degree of mixing in polymerization reactions can be influenced by various factors that can also affect the reactor performance. For this reason, a detailed micromixing model was implemented to study the effects of micromixing on the dynamic behavior of continuous free-radical solution polymerization tank reactors. The reactor model was used to perform the bifurcation analysis of the reacting system, paying special attention to the effect of micromixing parameters on the reactor behavior. The bifurcation study showed that multiple steady-states and periodic oscillations can be observed under partially segregated micromixing conditions. Moreover, the micromixing model was able to describe the dynamic responses presented by perfectly mixed and completely segregated reactors. These results indicate that this class of reactors can exhibit more complex dynamic behavior than shown until now.     

Theoretical investigation of electro-osmotic flows and chaotic stirring in rectangular cavities

Two-dimensional, time-independent and time-dependent electro-osmotic flows driven by a uniform electric field in a closed rectangular cavity with uniform and non-uniform zeta potential distributions along the cavity’s walls are investigated theoretically. First, we derive an expression for the one-dimensional velocity and pressure profiles for a flow in a slender cavity with uniform (albeit possibly different) zeta potentials at its top and bottom walls. Subsequently, using the method of superposition, we compute the flow in a finite length cavity whose upper and lower walls are subjected to non-uniform zeta potentials. Although the solutions are in the form of infinite series, with appropriate modifications, the series converge rapidly, allowing one to compute the flow fields accurately while maintaining only a few terms in the series. Finally, we demonstrate that by time-wise periodic modulation of the zeta potential, one can induce chaotic advection in the cavity. Such chaotic flows can be used to stir and mix fluids. Since devices operating on this principle do not require any moving parts, they may be particularly suitable for microfluidic devices.     

Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.     

Magnetogasdynamic natural convection in a long vertical microchannel

Since the transport behavior of ionized gases at the microscale could be influenced by an applied magnetic field with ease, microscale magnetogasdynamics (MGD) promises to be particularly advantageous for magnetically controllable microfluidic devices. The purpose of this study is to investigate how magnetic force affects the MGD natural convection within a long asymmetrically heated vertical planar microchannel. The fully developed solutions of the thermal-flow fields and their characteristics are analytically derived on the basis of the first-order slip and jump boundary conditions and then presented for the thermophysical properties of ionized air at the standard reference state flowing through the microchannel with complete accommodation. The calculated results reveal that magnetic force plays a damping role in flow and results in decreases in flow rate, average flow drag, and average heat transfer rate. In addition, it is interesting that because the flow near the core is suppressed and the shear stress on the wall surface is reduced by the magnetic effects, a flatter velocity profile could be achieved by a greater magnetic force. These magnetic effects could be further magnified by increasing gas rarefaction or increasing cooler wall temperature.