Two immiscible non$-$Newtonian fluids are at rest between two stationary plates as shown below.

Due to the density difference the heavier fluid is at the bottom. Both fluids behavior can be

expressed by non$-$Newtonian power law and the flow consistency index is the same for both fluids.

Under certain pressure drop both fluids start to move from left to right. Assume that the fluids are in

laminar flow regime. What is the most probable velocity profile for the two fluids in motion

assuming that the steady state conditions have been achieved? Please sketch the velocity profile in

the figure below and justify.

Fluid A$,$ n$=1\mathrm{.}4$

Fluid B$,n=0\mathrm{.}6$