![]() This model is able to predict some general features typical of viscoelastic emulsions, such as shoulders in the storage modulus G ′ at low frequency and a long relaxation time process. A different expression which however provides similar predictions was later derived by Bousmina 24 who extended Kerner's model 22 for the flow of composite elastic media to emulsions of viscoelastic phases with interfacial tension undergoing small deformations. 22–24 Palierne 23 derived an expression to predict the shear modulus of emulsions of viscoelastic materials accounting for the mechanical interactions between inclusions. 20,21 Few theoretical expressions were proposed in the past to predict the rheology of viscoelastic emulsions. In this work, we account for the coalescence and study how it affects the rheology of emulsions adding an additional complexity to the system by considering non-Newtonian solvents. These previous studies were focused only on deforming droplets, without taking into account coalescence and breakup, which however plays a key role in the rheological behavior of emulsions and are the main elements distinguishing emulsions from particle suspensions. The sign change is caused by the increasing drop inclination in the presence of inertia, which in turn directly affects the interfacial stresses. ![]() ![]() ![]() 15 also investigated the inertial effects on emulsions and found that while in the absence of inertia emulsions display positive first and negative second normal stress differences, a small amount of inertia alters their signs with the first normal stress difference becoming negative and the second one positive. 14 Their results revealed the complexity of emulsions rheology, with pronounced shear-thinning and large normal stresses associated with an anisotropic microstructure resulting from the alignment of deformed drops in the flow direction. Zhou and Pozrikidis 13 simulated numerically two-dimensional emulsions and their work was later extended to three-dimensional flows by Loewenberg and Hinch. This process is independent of the nominal viscosity ratio of the two fluids and we show that it can not be understood by considering only the mean shear rate and viscosity of the two fluids across the domain, but the full spectrum of shear rate must be taken into account. The changes in the emulsion viscosity are mainly due to modifications of the coalescence in the system obtained by changing the carrier fluid property: indeed, local large and low shear rates are found in the regions between two interacting droplets for shear-thickening and thinning fluids, respectively, resulting in increased and reduced local viscosity which ultimately affects the drainage time of the system. We show that the effective viscosity of the system increases for shear-thickening fluids and decreases for the shear-thinning ones for all the viscosity ratios considered. Several carrier fluids are considered encompassing both the shear-thinning and thickening behaviors. The analysis is performed for different volume fractions and viscosity ratios under the assumption of negligible inertia and zero buoyancy force. The problem at hand is tackled by means of direct numerical simulations using the volume of fluid method. ![]() We study the rheology of a two-fluid emulsion in semiconcentrated conditions the solute is Newtonian while the solvent is an inelastic power-law fluid. ![]()
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