Semi-Analytical Solutions of Multilayer Flow of Viscous Fluids in a Channel

Multilayer unidirectional flows of viscous, immiscible fluids in a channel bounded by two infinite parallel plates are studied. The bottom plate is translating in its plane with a time-dependent velocity and the upper plate is stationary. A pressure gradient in the flow direction is applied. The solutions of the initial and boundary condition problem are obtained using the Laplace transform method. Numerical Stehfest's algorithm is used in order to obtain the inverse Laplace transforms. The case of two-layers with one fluid-fluid interface is completely studied and influence of the pressure gradient on the fluid behavior is analyzed.