Saffman-Taylor instability in a radial Hele-Shaw cell for a shear-dependent rheological fluid

Abstract

We present the study of viscous fingering in the radial hele shaw cell, using the shear-dependent rheological fluid which transitions from the Newtonian to shear thinning behaviour, at low shear rates. The experimental observations show that the characteristic features of the fingering phenomena in the case of shear-thinning flow (such as side branching, growth of second generation fingers, inhibition of tip splitting), is observed at late times, from an initial Newtonian regime. On account of the asymmetry of the fingering structure, the local shear rate is non-uniform. This leads to different rheological behaviour in different sections of the network locally, revealing contrasting local fingering patterns, specific to the respective fluid rheological state based on the local shear rate. This is also explained using the numerical simulations for such rheological fluid, in the two-phase porous media flow. The fingering features, such as the length, width are quantified as a function of the flowrate. We have also observed detachment of the fingers beyond a certain critical size of the fingering network. Finally, the stability of the fingering is also investigated at ultra low flow rates, which suggests that the duration of stability exists much beyond what is predicted using the linear stability analysis for classical Newtonian flows.