Assume laminar flow and derive the velocity profile 7 Two im

Assume laminar flow and derive the velocity profile 7. Two immiscible fluids of different density and viscosity are flowing between two parallel plates. Express the boundary conditions at the interface between the two fluids.

Solution

There must be compatibility conditions at the interface between the two fluids. We require that the velocity be continuous and that the shear stres be continuous (otherwise there would be generation of momentum at the interface).

Hence, the boundary conditions would be,

V₁(h₁) = V₂(h₂)

and u₁(dV₁ / dx)_@h1 = u₂(dV₂ / dx)_@h1

Here..h1 is the location of the interface, x is the longitudinal direction, u1 and u2 are the absolute viscosities of the two fluids and V1, V2 are the velocities of the two fluids.