Linear hydrodynamic stability theory for thin film flow down cones and cylinders

The effect of the nonparallel nature of the basic flow on the stability of thin film flow down a cone is studied. The resulting basic flow equations and also the linearized stability equations are partial differential equations, in contrast to the classical stability studies where these equations are ordinary differential equations. An analytical solution to the linear stability problem for a nonparallel film flow was obtained using a regular perturbation expansion in a small parameter which is a measure of the characteristic length for diffusion of vorticity in the cross stream direction to the characteristic length in the streamwise direction.