Abstract: We
examine the linear stability to axisymmetric
disturbances in weakly rarefied flows (‘slip
regime’) in microchannels. A semi-analytical
solution of the Orr-Sommerfeld equation shows
that pulsatile flow is linearly stable in the
slip regime although a sudden change in the
stability properties of the flow occurs at a
critical value of the Knudsen number Kncr
= (2 – s)/8s,where
s
is the accommodation coefficient. Flow
structures corresponding to the largest energy
growth are toroidal vortex tubes that are
transported diffusively and convectively by
the mean flow. Transient energy growth is
found to decrease for Knudsen numbers Kn
< Kncrdue
to the diminished wall vorticity induced by
the slip conditions. Thus the Orr-Sommerfeld
operator for slip flow is less non-normal
compared to continuum-based no-slip flows.
Keywords and phrases: slip flow, stability, pulsatile pipe flow, Orr-Sommerfeld operator, Galerkin projection, non-normality, vortex tubes, energy growth.
