Steady and transient thin-jet flow of a viscoelastic fluid

Steady and transient two-dimensional thin-jet flow of a viscoelastic is examined theoretically. The influence of inertia, elasticity, and gravity is emphasized. The fluid is assumed to emerge from a vertical channel and to be driven by a pressure gradient and/or gravity. The boundary-layer equations are generalized for a viscoelastic thin film obeying the Oldroyd-B constitutive model. In contrast to the commonly used depth-averaging solution method, the strong nonlinearities are preserved in the present formulation as the viscoelastic boundary-layer equations are solved by expanding the flow field in terms of orthonormal shape functions. It is found that elasticity and gravity have the most profound effect on the steady state as well as the transient behavior of the viscoelastic film. The initial conditions strongly determine the stability of the film, which for all transient cases examined were shown to be stable despite the presence of initial instabilities.