An analytical comprehensive solution for the superficial waves appearing in gravity-driven flows of liquid films

作     者：Chimetta, Bruno Pelisson Franklin, Erick 

作者机构：UNICAMP Univ Campinas Sch Mech Engn Rua Mendeleyev 200 BR-13083860 Campinas Brazil 

出 版 物：《ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK》 (应用数学与物理学杂志)

年 卷 期：2020年第71卷第4期

页      面：122-122页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior - Brasil (CAPES) Fundacao de Amparo a Pesquisa do Estado de Sao Paulo - FAPESP [2018/14981-7] Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - CNPq [400284/2016-2] Fundo de Apoio ao Ensino, Pesquisa e Extensao da Unicamp - FAEPEX/UNICAMP [2112/19] 

主　　题：Gravity-driven flow Generalized Newtonian fluid Carreau-Yasuda model Temporal stability Asymptotic method 

摘      要：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 supposinga priorithe 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.