EVENT DETAILS AND ABSTRACT

Title: The Sharp Interface Limit of Hydrodynamics for Immiscible Flows
Speaker: Professor Yaguang Wang,
Speaker Info: Northwestern University and Shanghai Jiao Tong University
Brief Description:
Special Note:
Abstract:

In this talk, we are interested in the asymptotic analysis for the dynamics of two immiscible incompressible fluids moving in a channel, which is described by a problem for the Cahn-Hilliard and Navier-Stokes coupled equations with the velocity obeying a generalized Navier boundary condition. By formal analysis, we conclude that the leading profiles of the sharp interface limit satisfy a boundary value problem for the Hale-Shaw and Navier-Stokes coupled equations with the interface being a free boundary, and the leading contact angle between the interface and the physical boundary equals to the static one satisfying the Young law. We obtain an explicit formula of the main error between the dynamic angle and the static angle, which depends on the structure of the inner layer on the interface. Furthermore, we have also studied this problem when the thickness of the interface between fluids and the viscosity of fluids go to zero simultaneously. In this case, there exists an interaction between inner layers and boundary layers for the velocity profiles.