Instability of Thin Liquid Films Falling Down Inclined Walls: Instability Tested for a Variety of Wall Boundary Conditions

摘要

In this paper a review of the flow instability of thin films flowingdown walls is presented. Papers found in the literature considered fundamental are discussed with the basic equations relevant to the problem. However, stress will be given to the work done by the author during several years on thin films subjected to a variety of boundary conditions. After an introduction, a description of the linear and nonlinear theories, in particular the theory leading to the nonlinear Benney equation, are developed under the small wave number approximation. Next, the linear and nonlinear theories related with the instability of films flowing down rotating walls are discussed. Besides, the theory of fluid films affected by thermocapillarity due to a temperature gradient across the layer is given. Finally, a theory on the instability of fluid layers flowing down smoothly deformed walls is presented.