Electrostatic Effects on Linear and Nonlinear Waves in Hanging Film Flows
Electrostatic Effects on Linear and Nonlinear Waves in Hanging Film Flows
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静电对悬膜流中线性和非线性波的影响
DOI：
10.1016/j.piutam.2014.01.048
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Hunt M
中科院分区：
文献类型：
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作者：
Hunt M
研究了液体膜润湿半无限水平基底底面的动力学。重力使薄膜不稳定，这项工作的目的是通过使用水平电场来控制这种不稳定性。薄膜湿润半无限大的介电固体块，其下以空气为界。来自这两个区域的电场与液膜中的电场耦合，并通过在应力张量中引入电麦克斯韦应力，通过界面边界条件对流体力学做出贡献。因此，出现了新的非局部项，并通过推导描述膜中界面位置和领先级水平速度的长波一维演化方程系统，在线性和非线性两方面研究了它们的影响。当表面张力存在时，存在一个不稳定波数带，使薄膜长波不稳定。结果表明，随着电场强度的增加，该带的大小逐渐减小到零（物理上这意味着任何有限水平长度的系统都可以被足够强的电场完全稳定）。所导出的非线性系统支持以永久行波形式存在的非线性相干结构，并在一定参数范围内对其解进行了数值计算。这种行波的产生可能有助于提高悬膜系统的输运特性。
The dynamics of a liquid film wetting the underside of a semi-infinite horizontal substrate are investigated. Gravity causes the film to be unstable and the objective of this work is to control such instabilities by using horizontal electric fields. The film wets a semi-infinite dielectric solid block and is bounded below by air. The electric fields from these two regions are coupled to those in the liquid film and contribute to the hydrodynamics through the interfacial boundary conditions by introducing electric Maxwell stresses in the stress tensor. As a result novel nonlocal terms arise and their effect is studied both in the linear regime as well as nonlinearly through a derivation of a system of long-wave one-dimensional evolution equations describing the interfacial position and the leading order horizontal velocity in the film. When surface tension is present there exists a band of unstable wavenumbers rendering the film long-wave unstable. It is shown that the size of this band decreases asymptotically to zero as the electric field strength is increased (physically this means that any system of finite horizontal length can be fully stabilized by a sufficiently strong electric field). The derived nonlinear system supports nonlinear coherent structures in the form of traveling waves of permanent form, and such solutions are computed numerically for a range of parameters. The production of such traveling waves may be useful in enhancing the transport properties in hanging film systems.