Studies on hydrodynamic stability of viscoelastic flows in a Hele-Shaw cell.

We will present some recent results on the stability of Multi-Layer Hele-Shaw flows of viscoelastic fluids in a Hele-Shaw cell. We will consider displacement studies of one viscoelastic fluid by another one, where either of the fluids can be upper-convected Maxwell, Oldroyd-B or Newtonian. This will build on our previous works [1]. We will give refinements of earlier works and present some new results missing in the works of Wilson [2].
[1] Prabir Daripa, “Instability of displacement of an Oldroyd-B fluid by air in a Hele-Shaw cell”, APS March Meeting 2014, Denver, CO, (March 03-07, 2014).
[2] S. Wilson, “The Taylor-Saffman Problem for a Non-Newtonian Liquid", Journal of Fluid Mechanics 220 (Nov. 1990), pp. 413-425.