On the stability of microchannel flow

A numerical investigation of the spectra of the Orr-Sommerfeld equation for plane Poiseuille flow in macro and micro channels is presented. The numerical approach is a modified method (with complex matrix pre-conditioning) to Orszag's (1971) pioneering approach. The results are compared with polar fluid where couple stresses effect is important. Both effects: couple stresses and velocity slip, are roughly equivalent to an apparent increase in the fluid viscosity. However, the slip-flow effect becomes more dominant as the channel size decreases and the critical Reynolds number decreases