Low Reynolds number film flow down a three-dimensional bumpy surface

The slow film flow down a doubly periodic bumpy surface is studied for the first time. Perturbations on the primary variables and the complex boundary conditions lead to a system of successive equations. The secondary flow and the free surface shape depend on the wavelength of the bumps and a surface tension-inclination parameter There exists an optimum aspect ratio of the protuberances for maximal flow rate. [DOI: 10.1115/1.2060730]