Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants

Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present both at the free surface and in the bulk of the fluid, and that conversion from one species to the other is possible. The surfactants couple to the fluid dynamics through the coefficient of surface tension, which depends on the surface density of surfactants. Gradients in this concentration give rise to Marangoni stress on the free surface. In turn, the fluid advects the surfactants and distorts their concentration through geometric distortions of the free surface. We model the surfactants in a way that allows absorption and desorption of surfactant between the surface and bulk. We prove that small perturbations of the equilibrium solutions give rise to global-in-time solutions that decay to equilibrium at an exponential rate. This establishes the asymptotic stability of the equilibrium solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants

Tice, Ian; Wu, Lei
Acta Applicandae Mathematicae , Volume 161 (1) – Jul 23, 2018
Download PDF
36 pages

Loading next page...
 
/lp/springer-journals/dynamics-and-stability-of-surface-waves-with-bulk-soluble-surfactants-PvQV0hsvQF

References (26)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Nature B.V.
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-018-0203-0
Publisher site
See Article on Publisher Site

Abstract

In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present both at the free surface and in the bulk of the fluid, and that conversion from one species to the other is possible. The surfactants couple to the fluid dynamics through the coefficient of surface tension, which depends on the surface density of surfactants. Gradients in this concentration give rise to Marangoni stress on the free surface. In turn, the fluid advects the surfactants and distorts their concentration through geometric distortions of the free surface. We model the surfactants in a way that allows absorption and desorption of surfactant between the surface and bulk. We prove that small perturbations of the equilibrium solutions give rise to global-in-time solutions that decay to equilibrium at an exponential rate. This establishes the asymptotic stability of the equilibrium solutions.

Journal

Acta Applicandae Mathematicae – Springer Journals

Published: Jul 23, 2018

There are no references for this article.