On a viscous two-fluid channel flow including evaporation

Abstract

In this contribution a particular plane steady-state channel flow including evaporation effects is investigated from analytical point of view. The channel is assumed to be horizontal. The motion of two heavy viscous immiscible fluids is governed by a free boundary value problem for a coupled system of Navier-Stokes and Stephan equations. The flow domain is unbounded in two directions and the free interface separating partially both liquids is semi-infinite, i.e. infinite in one direction. The free interface begins in some point Q where the half-line Σ1 separating the two parts of the channel in front of Q ends. Existence and uniqueness of a suitable solution in weighted HÖLDER spaces can be proved for small data (i.e. small fluxes) of the problem.

Keywords

• navier-stokes equations
• stephan equations
• free boundary value problem
• semi-infinite inner channel wall
• 35r35
• 35q30
• 76d03
• 76d05