Miscible displacements in capillary tubes: Influence of Korteweg stresses and divergence effects

Abstract

The question is addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations (Chen and Meiburg) and experiments (Petitjeans and Maxworthy) for miscible flows in capillary tubes. An estimate of the vorticity and stream function fields induced by the Korteweg stresses is presented, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, are seen to be very small, and they have a negligible influence on the tip velocity. As a result, we can conclude that they are not responsible for the discrepancies between experiments and conventional Stokes simulations.