On the Stability and Bifurcation of Marangoni Convection of Two Immiscible Liquids with a Nondeformable Interface

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-29 DOI:10.1137/23m1584174

Chao Xing, Daozhi Han, Quan Wang

引用次数: 0

Abstract

SIAM Journal on Applied Dynamical Systems, Volume 23, Issue 2, Page 1313-1344, June 2024.
Abstract.This article investigates the nonlinear stability and dynamic bifurcation for the equations governing the Marangoni convection of two superimposed immiscible liquids subject to temperature gradient perpendicular to the plate. First, we obtain the critical value of the Marangoni number and verify the stability exchange principle by adopting a hybrid method that combines theoretical analysis and numerical calculations. Second, we employ the energy method, probing the nonlinear stability and establishing the nonlinear thresholds of the Marangoni number. Third, we apply the technique of center manifold reduction to reduce the corresponding infinite-dimensional model to finite-dimensional ODEs. According to the ODEs, we establish a dynamic bifurcation theorem with the transition number that determines the bifurcation type of the model. Finally, we determine the nondimensional transition number and present related temporal and flow patterns by performing careful numerical computation.

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关于具有不可变形界面的两种不相溶液体的马兰戈尼对流的稳定性和分岔问题

SIAM 应用动力系统期刊》，第 23 卷第 2 期，第 1313-1344 页，2024 年 6 月。摘要：本文研究了温度梯度垂直于板面的两种叠加不相溶液体马兰戈尼对流方程的非线性稳定性和动力学分岔。首先，我们采用理论分析与数值计算相结合的混合方法，得到了马兰戈尼数的临界值，并验证了稳定性交换原理。其次，我们采用能量法，探测非线性稳定性并建立马兰戈尼数的非线性临界值。第三，我们运用中心流形还原技术，将相应的无穷维模型还原为有限维 ODE。根据 ODE，我们建立了动态分岔定理，其过渡数决定了模型的分岔类型。最后，通过细致的数值计算，我们确定了非维度转换数，并提出了相关的时间和流动模式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.