PRESSURE-DRIVEN FLOW OF A THIN VISCOUS SHEET

Systematic asymptotic expansions are used to find the leading-order eq uations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatu res, the Navier-Stokes equations with appropriate free-surface conditi ons are simplified to give a 'shell-theory' model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to b e employed. The effects of surface tension, gravity and inertia can al so be incorporated in the model.