Squeeze-film flow of a viscoelastic fluid a lubrication model (Q1119079)

In this paper the constant-speed squeezing flow of a model viscoelastic fluid which allows for a Carreau-type viscosity and a stress overshoot in a startup of a shear flow is considered. Based on the knowledge of the full numerical solution by a boundary element method a set of lubrication equations is constructed which we believe to retain all the essential physics. The lubrication equations consist of four partial differential equations in time and one spatial coordinate. These are more tractable than the full set of governing equations (partial differential equations in time and two spatial coordinates). The lubrication equations are solved by a finite difference scheme, and the results are compared favourably with the full numerical solutions. The mechanism for load enhancement is also discussed.