Variational Approach in Two-Phase Flows of Complex Fluids: Transport and Induced Elastic Stress

Chun Liu, Jie Shen, James J. Feng & Pengtao Yue

Mathematical Models and Methods in Phase Transitions,
editor: Alain Miranville
Chapter 11, pp. 259-278. Nova Publishers, New York (2005).

Abstract - A general variational approach for the study of mixtures of complex fluids is described in this paper. In particular, the special coupling between the transport of the microscopic variables by the flow and the induced elastic stress is elaborated, and an efficient numerical scheme based on a stabilized semi-implicit discretization in time and a well-conditioned spectral-Galerkin method in space is also presented. As examples of applications, the Marangoni-Benard convection and the mixture of nematic liquid crystal with a Newtonian fluid are considered. Some numerical simulations indicating the robustness and versatility of the proposed approach are presented.