Fluid injection model without surface tension for resins in thin molds

The aim of this article is to propose a simple mathematical model providing the mean evolution of the interface between two fluids, the injected one and the other one initially filling the mold when the surface tension is neglected. Then using the asymptotic expansion we obtain a conservation law, describing the evolution of the free boundary between the fluids. A Riemannʹs problem for the nonlinear hyperbolic equation for the free boundary describes the injection as a rarefaction wave for the saturation which admits three kind of solution parameterized by the ratio of viscosities. If the mobility ratio is null, we prove that the interface is not attached at the inlet of the mold.