Perturbation analysis of liquid flows in micro-channels driven by high pressures

An asymptotic expansion of compressible N-S equations were deduced via parametric expansion, and liquid flow characteristics under high driven pressures in long micro-channels with arbitrary cross sections were analyzed by solving the zeroth order equations. The contributions due to cross section, length of the wall-slip, and other related factors were taken into account by solving the Green's function over the cross section. A set of zeroth order solutions for circular cylinders of constant cross section were presented, and the influences of the compressibility and viscosity of the liquids, and the slip length on the flow characteristics in micro-channels under high pressure were studies.