Creeping flow analyses of free surface cavity flows

Two industrially important free surface flows arising in polymer processing and thin film coating applications are modelled as lid-driven cavity problems to which a creeping flow analysis is applied. Each is formulated as a biharmonic boundary-value problem and solved both analytically and numerically. The analytical solutions take the form of a truncated biharmonic series of eigenfunctions for the streamfunction, while numerical results are obtained using a linear, finite-element formulation of the governing equations written in terms of both the streamfunction and vorticity. A key feature of the latter is that problems associated with singularities are alleviated by expanding the solution there in a series of separated eigenfunctions. Both sets of results are found to be in extremely good agreement and reveal distinctive flow transformations that occur as the operating parameters are varied. They also compare well with other published work and experimental observation.