悬浮液膜中的旋转电流体动力学流动
Rotating electrohydrodynamic flow in a suspended liquid film
摘要：
本文提出并研究了悬浮液膜中旋转电流体动力学流动的数学模型。该运动由在一个方向上的给定电势差和在膜平面中的另一个方向上的恒定外部电场$\vE_\text{out}$驱动。为了推导出该模型，我们采用了空间平均法的正常坐标的膜，导致平均雷诺应力是成比例的$|\vE_\text{out}|^3$。该应力在膜的边缘附近产生切向速度，这又引起液体的旋转运动。提出的模型旨在解释\emph{liquid film motor}的实验观察结果（参见arXiv：0805.0490 v2）。
英文摘要：
The mathematical model of a rotating electrohydrodynamic flow in a thin suspended liquid film is proposed and studied. The motion is driven by the given difference of potentials in one direction and constant external electrical field $\vE_\text{out}$ in another direction in the plane of a film. To derive the model we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to $|\vE_\text{out}|^3$. This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is aimed to explain the experimental observations of the \emph{liquid film motor} (see arXiv:0805.0490v2).
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