Viscous flow between two moving parallel disks: exact solutions and stability analysis

Abstract

The motion of a viscous incompressible liquid between two parallel disks, moving towards each other or in opposite directions, is considered. The description of possible conditions of motion is based on the exact solution of the Navier–Stokes equations. Both stationary and transient cases have been considered. The stability of the motion is analysed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.