Refined two-dimensional models for the analysis of free boundary flows between parallel plates Original Research Article

We derive a hierarchy of dimensionally reduced models of Stokes flow in a narrow cavity. The models are obtained applying a method that combines features of both asymptotic and projection methods. The first model of this hierarchy is the Hele-Shaw model, the second model is capable of capturing three-dimensional effects such as the fountain effect. A free boundary problem assuming both a plane and parabolic flow front is solved. The results are compared with numerical solutions of Stokes equations.