Viscous fingering regimes in elasto-visco-plastic fluids

We experimentally study the Saffman-Taylor instability of air invasion into a non-Newtonian fluid (i.e., Carbopol solution) in a rectangular Hele-Shaw cell. In addition to viscous features, the non-Newtonian fluid used exhibits yield stress, shear-thinning as well as elastic behaviors. The key dimensionless parameters that govern the various flow regimes are the Bingham number (Bn), the capillary number (Ca), the Weber number (We), the Weissenberg number (Wi), the channel aspect ratio (δ ≫ 1), and the shear-thinning power-law index (n). Three main flow regimes are observed, i.e., a yield stress regime, a viscous regime and an elasto-inertial regime. We present a detailed description for each regime and quantify their transition boundaries versus dimensionless groups. Some of the secondary flow aspects, e.g., the wall residual layer thickness and a network structure regime, have been also studied.