We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in a vertical magnetic field. The arising Lorentz force drives the electrolyte in the plane of the layer. We employ the long-wave approximation to derive general two-dimensional hydrodynamic equations describing symmetric pinching-type deformations of the free surfaces. These equations are used to study the azimuthal flow in an annular film spanning the gap between two coaxial cylindrical electrodes. In weakly deformed films, the base azimuthal flow and its linear stability with respect to azimuthally invariant perturbations are studied analytically. For relatively thick layers and weak magnetic fields, the leading mode with the smallest decay rate is found to correspond to a monotonic azimuthal velocity perturbation. The Marangoni effect leads to further stabilisation of the flow while perturbations of the solute concentration in the bulk of the fluid have no influence on the flow stability. In strongly deformed films in the diffusion-dominated regime, the azimuthal flow becomes linearly unstable with respect to an oscillatory mixed mode characterised by the combination of radial and azimuthal velocity perturbations when the voltage applied between electrodes exceeds the critical value.

中文翻译：

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无支撑电解质层中的电磁驱动流动：润滑理论和环形流动的线性稳定性

我们考虑非磁性电解质的薄水平层，其中包含大量盐溶液并携带电流。该层以两个载有不溶性表面活性剂的可变形自由表面为界，并置于垂直磁场中。产生的洛伦兹力驱动层平面中的电解质。我们采用长波近似来推导描述自由表面对称收缩型变形的一般二维流体动力学方程。这些方程用于研究跨越两个同轴圆柱形电极之间间隙的环形薄膜中的方位流。在弱变形薄膜中，分析研究了基础方位角流及其相对于方位角不变扰动的线性稳定性。对于相对厚的层和弱磁场，发现具有最小衰减率的主模对应于单调方位角速度扰动。马兰戈尼效应导致流动进一步稳定，而大部分流体中溶质浓度的扰动对流动稳定性没有影响。在扩散主导区域的强烈变形薄膜中，当施加在电极之间的电压超过临界值时，方位角流动相对于以径向和方位角速度扰动的组合为特征的振荡混合模式变得线性不稳定。