Motion of Fluid Layers

This project investigates the flow of two parallel layers of oil and water which are located between two plates. Starting from the rest position the top plate is moved at a constant velocity which immediately affects the motion of the neighbouring oil layer. Eventually this will affect the motion of the lower water layer. A mathematical model is formulated which involves parabolic PDEs. Of course, the equations cannot be solved separately in the two layers because of the boundary conditions at the oil-water interface. A numerical solution is obtained using an implicit finite divided difference scheme in terms of time and space. In this way the velocity of the two fluid layers is obtained at various distances from the plates at different times. Clearly the effects of motion will be more noticeable as time proceeds. The results are validated against the steady state solution for large time.