Miscible displacements in capillary tubes: Effect of a preexisting wall film

Abstract

For miscible displacements in capillary tubes, the impact of a preexisting wall film on the tip velocity of the displacing fluid finger is analyzed by means of axisymmetric Stokes simulations. The wall film is assumed to have the same viscosity as the displacing fluid, which is less viscous than the displaced fluid. The finger of the displacing fluid is seen to move in a quasisteady fashion, with a tip velocity below the centerline velocity of an equivalent Poiseuille flow. The explanation for this behavior, which is in contrast to our earlier findings for miscible displacements without wall films, lies in the lubricating effect of the wall film. The condition is established for which the displaced fluid moves in a nearly solid body-like motion. In this limit, a closed expression is derived for the finger tip velocity. A comparison between the simulation data and the closed form results shows reasonable agreement, provided that the criterion for solid body-like motion is satisfied. Furthermore, results are presented for the practically relevant limit of large viscosity ratios.