Escandón Juan, Torres David, Hernández Clara, Vargas René
Instituto Politécnico Nacional, SEPI-ESIME Azcapotzalco, Departamento de Termofluidos, Av. de las Granjas No. 682, Col. Santa Catarina, Alcaldía Azcapotzalco, Ciudad de México 02250, Mexico.
Universidad Tecnológica de México -UNITEC MÉXICO- Campus Marina-Cuitláhuac, Ciudad de México 02870, Mexico.
Micromachines (Basel). 2020 Aug 5;11(8):757. doi: 10.3390/mi11080757.
In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers.
在本研究中，对狭缝微通道中多层不混溶粘弹性流体的瞬态电渗流进行了研究。通过将动量方程与麦克斯韦流体的流变模型进行适当组合，得到了一个双曲型偏微分方程，并采用拉普拉斯变换法对其进行半解析求解以描述速度场。在求解过程中，由于基于对称电解质的输送流体内容缓冲溶液，在液 - 液界面必须考虑不同的静电条件和电粘性应力。通过对控制方程和本构方程采用无量纲数学模型，出现了一些控制电渗流启动的无量纲参数，如粘度比、介电常数比、密度比、弛豫时间、电动参数和电位差。结果表明，由于粘性力和弹性力之间的竞争，速度在瞬态状态下呈现振荡行为；此外，流场受液 - 液界面的静电条件影响，产生陡峭的速度梯度，最后，达到稳态的时间强烈依赖于弛豫时间、粘度比和流体层数。
