Front dynamics in exchange flow of two immiscible iso-viscous fluids in two-dimensional straight and curved plane channels

Exchange flow of two immiscible fluids at a low Atwood number in a straight and curved plane channel is considered in this analytical study. The fluids are considered immiscible, but practically, the results can be applied to miscible fluids for short times and in nearly horizontal channels where mixing is negligible due to strong segregation. The exchange flow and displacement flow in pipes at different inclinations with respect to vertical have been extensively studied and have many applications in industry or environmental settings. For the case of plane two-dimensional channels, however, because of the simpler geometry, it is more convenient to understand the physics of the problem and formulate the physical phenomena mathematically. An equation has been derived that describes the transient front velocity in exchange flow in a straight plane channel. The steady state front velocity in straight channels is estimated. The exchange flow in curved channels demonstrates an unstable front or a separated trail because of the curvature of the path. In the case of curved channels, some of the general behavior of the interface is predicted and validated against some experimental observations in curved pipes but quantitative analysis of the interface and the flow requires more advanced mathematical formulation and more detailed experiments for validation.