Problems in the spreading and extrusion of a layer of non-linearly viscous fluid

Abstract

In the approximation of lubrication theory /1/, an equation is derived for the non-steady flow of a thin layer of a power-law liquid along a horizontal plane, when different conditions are assumed to hold at the upper boundary of the layer. Among the problems considered are the spread of an initially localized inhomogeneity, jet overflow, and spreading (extrusion) of a semi-infinite layer. Selfsimilar solutions are constructed for these problems describing waves propagating at finite velocities in the steady thickness region of the layer. Such situations occur in problems of tectonic physics /2/, glaciomechanics /3, 4/ and polymer technology /5, 6/. The more general problem of a layer flowing along a pliable base /2/ can be handled in exactly the same way.