Problem $2$:

Derive the equilibrium velocity distribution of the fluid flow between two infinite parallel plates subject to both pressure gradient $(-$del$\frac{P}{d}$elx$)$ and electroosmosis induced by an external field E$.$ Assume the gap between the plates are $2h>100{}_D.$ The electroosmotic mobility of the top and bottom plates are ${}_t$ and ${}_b$ respectively. Fluid viscosity is denoted with $.$