Instability of the displacement fronts of non-Newtonian fluids in a Hele-Shaw cell☆

Abstract The destabilizing effect of the shear-thinning of a non-Newtonian fluid and its elasticity in the plane-parallel and circular displacement fronts in a Hele-Shaw cell is investigated, as well as the influence of the elasticity of a fluid on the shape of the Saffman-Taylor “fingers” which are formed when primary instability develops in the fronts. The treatment is carried out separately for a pure viscous non-Newtonian fluid and for a visco-elastic fluid (with Newtonian viscous behaviour under steady shear flow). As a result of the multistage development of instability in the displacement of one fluid by another in a Hele-Shaw cell (as the flow in the narrow gap between large plane parallel plates is traditionallycalled), various structures can be formed from an individual displacement finger up to complex patterns of a fractal nature. The form of these structures and the conditions for their formation are found to be sensitive to the rheological characteristics of the fluids.