Some models for immiscible displacements in Hele-Shaw cells

Abstract

We study the linear stability of the immiscible displacement of some fluids in 2D and 3D Hele-Shaw cell. We give a method for avoiding the singularities phenomenons which appears in previous papers. In the case of a non - Newtonian fluid displaced by air in a 3D Hele-Shaw cell, we give a growth constant σ of perturbations, which contains two new terms compared with the Saffman-Taylor formula. Our σ has a very high growth as a parameter appearing in the constitutive relations approaches a critical value.

Keywords

• hele-shaw displacement
• non-newtonian uids
• linear stability
• dispersion formula