Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel

This study investigates the electromagnetohydrodynamic(EMHD)flow of fractional viscoelastic fluids through a microchannel under the Navier slip boundary condition.The flow is driven by the pressure gradient and electromagnetic force where the electric field is applied horizontally,and the magnetic field is vertically(upward or downward).When the electric field direction is consistent with the pressure gradient direction,the changes of the steady flow rate and velocity with the Hartmann number Ha are irrelevant to the direction of the magnetic field(upward or downward).The steady flow rate decreases monotonically to zero with the increase in Ha.In contrast,when the direction of the electric field differs from the pressure gradient direction,the flow behavior depends on the direction of the magnetic field,i.e.,symmetry breaking occurs.Specifically,when the magnetic field is vertically upward,the steady flow rate increases first and then decreases with Ha.When the magnetic field is reversed,the steady flow rate first reduces to zero as Ha increases from zero.As Ha continues to increase,the steady flow rate(velocity)increases in the opposite direction and then decreases,and finally drops to zero for larger Ha.The increase in the fractional calculus parameterαor Deborah number De makes it take longer for the flow rate(velocity)to reach the steady state.In addition,the increase in the strength of the magnetic field or electric field,or in the pressure gradient tends to accelerate the slip velocity at the walls.On the other hand,the increase in the thickness of the electric double-layer tends to reduce it.

Vlasov方程的精确解

该文将等熵磁流体力学（ＭＨＤ）或等熵电磁流体力学（ＥＭＨＤ）的基本方程组以及（非相对论的或相对论的）Ｖｌａｓｏｖ方程，分别化为等熵流体力学（ＨＤ）表象，建立了上述三类等熵方程之间的对应关系．从而使非相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＭＨＤ方程的精确解相对应）和相对论Ｖｌａｓｏｖ方程的精确解（它与等熵ＥＭＨＤ方程的精确解相对应）都可以用（非相对论的和相对论的）等熵ＨＤ方程的精确解来表示．

电磁激活板的宽度对圆柱绕流控制的影响

电磁力可以改变流体边界层的结构,是控制流体运动的主动控制方法之一。基于电磁场和流体的基本方程,对置于弱电介质中的圆柱电磁激活板周围产生的Lorentz力及其对圆柱绕流的控制进行了数值模拟,着重讨论了电磁激活板的宽度对其周围的电磁场、产生的Lorentz力、流场的控制和涡量变化的影响。电磁场包覆范围为流体分离点至其后部,当N值较小时,分离点后移,但不能够完全抑制流体的分离,极板越宽对尾涡的抑制效果越好;随着N值的增大,由于极板窄的表面涡量大,所以可以首先达到完全抑制流体分离的控制效果;当N值较大时,无论极板宽窄,都可以达到完全抑制流体分离的效果。

电磁体积力作用下的圆柱绕流实验研究

利用电介质溶液中圆柱体侧表面附近分布的电磁场产生电磁体积力,作用于流体边界层,从而控制圆柱绕流。电极与磁极交替分布的电磁场激活板包覆在圆柱体表面置于流动的电解质溶液中,产生的电磁力沿圆柱体表面分布,可以改变流体边界层结构。在流体边界层上电磁体积力的作用下,圆柱绕流分离点可以在前驻点和后驻点之间变动,产生不同的控制效果。调整电磁场的时空分布控制参数,电磁体积力能连续控制圆柱绕流、尾流涡街的形态,具有明显的消涡与增涡控制效应;具有较好的减震、减阻控制效果;具有制动控制效应。

Electroviscous effect on electromagnetohydrodynamic flows of Maxwell fluids in parallel plate microchannels

Considering the influence of the streaming potential and electroviscous effects, the analytical solutions for electromagnetohydrodynamic (EMHD) flows in parallel plate microchannels are obtained. The electrolyte solutions in the microchannels are taken as generalized Maxwell fluids, and slip boundary conditions are adopted. To accurately analyze the EMHD flow characteristics, the variation trends of the electroviscous effects with the corresponding parameters must be understood. The results show that the electroviscous effects increase with the increase in the relaxation time De, the slip coefficient , and the wall zeta potential 0. However, the increase in the inverse of the electrical double-layer (EDL) thickness K, the electrical oscillating Reynolds number Re, and the ionic P'eclet number Pe can decrease the electroviscous effects. We also demonstrate that the electroviscous effect on the EMHD flows of generalized Maxwell fluids is larger than that of Newtonian fluids. This work will be useful in designing EMHD flows in parallel plate microchannels.

Electromagnetohydrodynamic flows and mass transport in curved rectangular microchannels

Curved microchannels are often encountered in lab-on-chip systems because the effective axial channel lengths of such channels are often larger than those of straight microchannels for a given per unit chip length.In this paper,the effective diffusivity of a neutral solute in an oscillating electromagnetohydrodynamic(EMHD)flow through a curved rectangular microchannel is investigated theoretically.The flow is assumed as a creeping flow due to the extremely low Reynolds number in such microflow systems.Through the theoretical analysis,we find that the effective diffusivity primarily depends on five dimensionless parameters,i.e.,the curvature ratio of the curved channel,the Schmidt number,the tidal displacement,the angular Reynolds number,and the dimensionless electric field strength parameter.Based on the obtained results,we can precisely control the mass transfer characteristics of the EMHD flow in a curved rectangular microchannel by appropriately altering the corresponding parameter values.

Effect of patterned hydrodynamic slip on electromagnetohydrodynamic flow in parallel plate microchannel

A fully developed electromagnetohydrodynamic(EMHD) flow through a microchannel with patterned hydrodynamic slippage on the channel wall is studied. The flow is driven by the Lorentz force which originates from the interaction between an externally imposed lateral electric field and a perpendicular magnetic field. The governing equations for the velocity with patterned slip boundary conditions are solved analytically by perturbation techniques under the assumption of small Reynolds number Re. In addition, the numerical solutions for the velocity are obtained by using the finite-difference method, and they are found to be in good agreement with the analytical solutions within admissible parameter range. The effects of different parameters on the velocity and volume flow rate due to patterned hydrodynamic slippage are discussed in detail, including wave-number K, Hartmann number Ha, amplitude δ of the patterned slip length, and normalized electric field strength S. The results show that patterned slippage over microchannel walls can induce transverse flows, which will increase the mixing rates in microfluidic devices. In addition, we also find that precise flow control can be achieved by controlling the magnetic flux and the wave-number and also by well choosing the electric field intensity. Our analysis can be used for designing the efficient micro-fluidic mixers.

平行板微管道内的Jeffrey流体的电磁流动

研究了平行板微管道内线性黏弹性流体的电磁流动,其中线性黏弹性流体的本构关系是由Jeffrey流体模型来描述的。利用分离变量法,在无滑移条件和滑移条件下,求解了线性化的非定常柯西动量方程和Jeffrey流体本构方程,给出了黏弹性Jeffrey流体速度的解析表达式。通过数值计算,分析了无量纲雷诺数Re、哈特曼数Ha、弛豫时间λ1ω和滞后时间λ2ω对速度剖面的影响。结果表明,无量纲滑移长度α增大了流体的速度振幅,滑移条件下流体的速度大于无滑移条件下流体的速度。此外,随着哈特曼数Ha的增加,速度先增加后减少;随着弛豫时间λ1ω的增加,速度也变得越来越大;随着雷诺数Re和滞后时间λ2ω的增加,速度变得越来越小。

基于伴随流场的流动优化控制

弱电介质溶液中,电磁场产生的Lorentz力可以控制流体的运动。将其用于钝体绕流时,可以减少阻力、抑制分离和消除涡街。该文根据非线性优化控制理论,以圆柱绕流的电磁优化控制为例,以控制涡能为目的,推导了性能指标的表达式和伴随方程。基于棋手对弈时选择最佳落子的思路,通过求解流动方程和伴随方程,得到流场的非线性优化控制的解,即优化的电磁场强度的变化规律。讨论了优化控制下,绕流流场和圆柱表面阻力和升力的变化。结果表明:通过优化控制,可以达到减少阻力、消除涡街及涡生振荡的目的。