Thin film limit and film rupture of the visco-capillary gravity-driven channel flow

Starting from an exact solution of a visco-capillary gravity-driven film flow of a Newtonian fluid in an inclined channel, we discuss the special case of thin films. The shape of the free surface, the velocity field and the flow rate are obtained from a pure analytical treatment. Making use of an adequate rescaling with a generalized capillary length we pay special attention to vanishingly thin films where capillary effects become dominant. Our investigations deliver a necessary condition for the flow rate in order to avoid a film rupture.