Instability of Poiseuille flow of two immiscible liquids with different viscosities in a channel (Q1822576)

This is a stability analysis of plane Poiseuille flow of two immiscible liquids of different viscosities and equal densities. It is considered the case of three layers with one of the fluids centrally located. Experiments have shown that there is a tendency of the less viscous fluid to encapsulate the more viscous one. Such an arrangement obeys the ''viscous dissipation principle''. A linear stability analysis to long waves is carried out and it is studied the dependence on viscosity and volume ratio. It is found that the flow with the high viscosity fluid centrally located is always stable and centrally located layers of less viscous fluid (fingering flows) are always unstable.