Stability and evolution of a dry spot

The motion of a thin viscous layer of fluid on a horizontal solid surface bounded laterally by a dry spot and a vertical solid wall is considered. A lubrication model with contact line motion is studied. We find that for a container of fixed length the axisymmetric equilibrium solutions with small dry spots are unstable to axisymmetric disturbances. As the size of the dry spot increases, the equilibrium solutions become unstable to nonaxisymmetric disturbances. In addition, we present numerical solutions of the nonlinear evolution equations in the axisymmetric and nonaxisymmetric cases for different values of the parameters. The axisymmetric results show good agreement with existing experimental results.