Displacement flows between Newtonian fluids at moderate Reynolds numbers in rectangular channels

Displacement flows between two Newtonian fluids in rectangular channels is studied by numerical and analytical means. Two-stages are clearly seen in the displacement process: first, a core of the displaced fluid is removed by a finger of the displacing fluid with width less than the channel height; then, the film of the displaced fluid adjacent to the wall left behind is then removed via interfacial instabilities that grow spatio-temporally. The shape of the finger dictated by a meniscus in the front and a tail of nearly asymptotic height; the latter is a function of the viscosity and density ratios, Weber number and Reynolds number. This dependence is studied by means of highly resolved direct numerical simulations using the diffuse-interface method. The interface shapes obtained is compared with analytical steady state solutions of the meniscus shapes in the downstream region and the asymptotic film thickness in the upstream region.