Transient free-surface flow inside thin cavities of viscoelastic fluids

The lubrication theory is extended for the flow of viscoelastic fluids of t he Oldroyd-B type inside thin cavities. The formulation accounts for nonlin earities stemming from inertia effects in the momentum conservation equatio n, and the upper-convected terms in the constitutive equation. The theory i s applied to transient free-surface-flow problems inside a thin (two-dimens ional) channel. The influence of fluid elasticity (Deborah number) and reta rdation on the shape and evolution of the front is examined. It is found th at the mean position of the front is dictated by a nonlinear equation of se cond order. The multiple-scale method is applied to obtain an approximate s olution at small Deborah number. Given the existence of a singularity in th e limit De --> 0, regular perturbation theory cannot be applied. Comparison with exact (numerical) solution indicates a wide range of validity for the multiple-scale results, which is not necessarily restricted to weakly elas tic flows. (C) 2000 Elsevier Science B.V. All rights reserved.