Real variable Hele-Shaw problem with kinetic undercooling

Abstract

It is considered the (slow) flow of the viscous incompressible fluid in the Hele-Shaw cell at presence of a rigid obstacle in the flow. A novel model for such a flow is proposed in terms of the parametrization of the boundary of the fluid front and Green’s function (or the Robin–Neumann function) for the Laplace equation in a doubly connected domain subject of the mixed boundary value problem (the Neumann problem on the boundary of the obstacle and the Robin problem on the fluid front). Preliminary results for asymptotic study of such Green’s function are presented too.