Displacement of a viscoplastic fluid in an inclined slot

Abstract

The steady displacement of one viscoplastic fluid by another is studied in an inclined channel. The aim is a prediction of the finger width from simple balance laws. It is argued that no accurate prediction can be acquired from the far field velocity profiles only, but that instead a calculation of the two dimensional behaviour near the free interface is needed. It is suggested that the static residual thickness can be determined from a minimization procedure for the dissipation in the system.