Linear Stability of Flows in a Squeeze Film

We study linear stability of viscous flows in a squeeze lubrication film, in which the flow varies slowly in space and time, between two parallel plates moving normal to each other with a slow constant speed, generalizing the inviscid results of Aristov and Gitman J. Fluid Mech. 464 (2002) 209. The temporal evolution of two-dimensional disturbances for this physical situation, including the asymptotic behaviour of a long term or the transient behaviour of some time interval, is obtained by the construction of a low-dimensional Galerkin method. It is found that the wall boundaries typically play dual roles of stabilizer and destabilizer. They constrain the development of disturbances and have stabilizing influences. However, they give rise to velocity shear, which is diffused by viscosity and thereby tends to destabilize the flow.