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We study the rheology of a two-fluid emulsion in semi-concentratedconditions; the solute is Newtonian while the solvent an inelastic power lawfluid. The problem at hand is tackled by means of direct numerical simulationsusing the volume of fluid method. The analysis is performed for differentvolume fractions and viscosity ratios under the assumption of negligibleinertia and zero buoyancy force. Several carrier fluids are consideredencompassing both the shear-thinning and thickening behaviors. We show that theeffective viscosity of the system increases for shear-thickening fluids anddecreases for the shear-thinning ones for all the viscosity ratios considered.The changes in the emulsion viscosity are mainly due to modifications of thecoalescence in the system obtained by changing the carrier fluid property:indeed, local large and low shear rates are found in the regions between twointeracting droplets for shear-thickening and thinning fluids, respectively,resulting in increased and reduced local viscosity which ultimately affects thedrainage time of the system. This process is independent of the nominalviscosity ratio of the two fluids and we show that it can not be understood byconsidering only the mean shear rate and viscosity of the two fluids across thedomain, but the full spectrum of shear rate must be taken into account.

Shear-thinning and shear-thickening emulsions in shear flows