Occurrence of coexisting dendrite morphologies: immiscible fluid displacement in an anisotropic radial Hele-Shaw cell under a high flow rate regime

Abstract

Viscous fingering morphologies during the displacement of a high viscosity fluid by a low viscosity immiscible fluid in a radial fourfold anisotropic Hele-Shaw cell are examined. By using the kerosene-glycerin system for which the mu/T ratio (mu being the relative viscosity and T the interfacial tension between the fluids) is about ten times higher than that for the commonly used air-glycerin system, we have been able to access the hitherto unexplored Nca greater than approximately 1 regime (capillary number Nca = U mu/T, U being the advancing fingertip velocity). Within the anisotropy-dominated regime, and when flow rates are significantly high (capillary number well beyond Nca = 1), a new phase is seen to evolve wherein the dendrites grow simultaneously along the channels and along the directions making an angle of 45 degrees with the channels, both being kinetically driven. This new phase resembles the one observed in a miscible fluid system at all flow rates of the displacing fluid. [A. G. Banpurkar et al., Phys. Rev. E 59, 2188 (1999)].