论文标题
一种分析综合解决方案，用于出现在液体薄膜重力驱动流中的浅表波
An analytical comprehensive solution for the superficial waves appearing in gravity-driven flows of liquid films
论文作者
论文摘要
本文致力于分析解决方案，以当carreau-Yasuda模型给出流体流变学时，由重力驱动的液体膜的基本稳定性和时间稳定性，这是一种适用于不同类型的流体的一般描述。为了获得不稳定性发作的基本状态和关键条件，提出了两组渐近扩展，从中可以找到描述参考流以及不稳定性相位速度和增长速度的四个新方程。这些结果导致了临界雷诺数的方程式，这决定了落下膜不稳定性的条件。与以前的作品不同，本文提出了渐近解决方案，用于获得的生长速率，波长和不稳定性，而不假设先验精确的流体流变学，因此对不同种类的流体有效。我们的发现是理解非牛顿流体重力流的稳定性的重要一步。
This paper is devoted to analytical solutions for the base flow and temporal stability of a liquid film driven by gravity over an inclined plane when the fluid rheology is given by the Carreau-Yasuda model, a general description that applies to different types of fluids. In order to obtain the base state and critical conditions for the onset of instabilities, two sets of asymptotic expansions are proposed, from which it is possible to find four new equations describing the reference flow and the phase speed and growth rate of instabilities. These results lead to an equation for the critical Reynolds number, which dictates the conditions for the onset of the instabilities of a falling film. Different from previous works, this paper presents asymptotic solutions for the growth rate, wavelength and celerity of instabilities obtained without supposing a priori the exact fluid rheology, being, therefore, valid for different kinds of fluids. Our findings represent a significant step toward understanding the stability of gravitational flows of non-Newtonian fluids.
