界面对微流控器件动力学特性的影响：滑移边界对极性液膜马达旋转特性的影响
Effects of interfaces on dynamics in micro-fluidic devices: slip-boundaries' impact on rotation characteristics of polar liquid film motors
摘要：
研究了极性液膜马达（PLFM）的滑移边界效应，该马达是一种新型的微流体器件，对提高液体微膜的结构、动力学、建模和工艺等方面的知识具有重要意义。我们开发了一个数学模型，滑移边界条件下，描述电流体动力学旋转的PLFM诱导的直流（DC）或交流（AC）领域。我们的主要结果是：（i）旋转特性取决于比率$k=l_{s}/D$（$l_{s}$表示滑移长度，由界面对液体结构的影响产生，$D$表示膜的直径）。(ii)作为$k$（$k>-1/2$）增大：（a）在“负"、“无"、“部分”和“完全”滑移边界条件下，PLFM均表现出旋转特性：（b）稳态旋转液膜线速度的最大值增大，且最大值的位置靠近液膜边界;（c）角速度对离膜中心的距离的依赖性的衰减减慢，导致边界附近的宏观流动。(iii)除了$k$之外，AC PLFM的旋转特性还取决于AC场的幅度、频率和相位差。(iv)我们的分析推导的转速分布与现有的实验结果是一致的。
英文摘要：
Slip-boundary effects on the polar liquid film motor (PLFM) -- a novel micro-fluidic device with important implications for advancing knowledge on liquid micro-film's structure, dynamics, modeling and technology -- are studied. We develop a mathematical model, under slip boundary conditions, describing electro-hydro-dynamical rotations in the PLFMs induced either by direct current (DC) or alternating current (AC) fields. Our main results are: (i) rotation characteristics depend on the ratio $k=l_{s}/D$ ($l_{s}$ denotes the slip length, resulting from the interface's impact on the structure of the liquid and $D$ denotes the film's diameter). (ii) As $k$ ($k>-1/2$) increases: (a) PLFMs subsequently exhibit rotation characteristics under "negative-", "no-", "partial-" and "perfect-" slip boundary conditions; (b) the maximum value of the linear velocity of the steady rotating liquid film increases and its location approaches the film's border; (c) the decay of the angular velocities' dependency on the distance from the center of the film slows down, resulting in a macroscopic flow near the boundary. (iii) In addition to $k$, the rotation characteristics of the AC PLFM depend on the magnitudes, the frequencies, and the phase difference of the AC fields. (iv) Our analytical derived rotation speed distributions are consistent with the existing experimental ones.
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