Some Hydrodynamic Models for Studying the Displacement of One Liquid by Another. Part II. Flow Within a Wedge
We construct and solve in an analytical way a model to describe the displacement process of one liquid by another. By neglecting surface tension and assuming simple shear flows, we find an explicit analytical solution for the time-dependent velocity profiles and discharges in a wedge-shaped geometry. Our formalism permits us to discern the presence of the 3 different time scales involved in this process that may have an influence over the whole displacement time. Finally, we discuss the qualitative similarity of this process and a diffusion process that has been used previously for fitting experimental results.
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