Surfaces that minimize area subject to various constraints have long been studied. Much of the inspiration for these studies has come from physical systems involving surface tension: soap films, soap bubbles, capillarity, biological cell structure, and others. So far, mathematical investigations have been mostly confined to the equilibrium states of the systems mentioned, with some study of the evolution of non-parametric hypersurfaces [LT]. This work studies in general dimensions a dynamic system: surfaces of no inertial mass driven by surface tension and opposed by frictional force proportional to velocity. The viewpoint is that of geometric measure theory