Towards a constitutive relation for emulsions exhibiting a yield stress

Constitutive relations are needed to predict the behavior of complex fluids in nonviscometric flows. This is an area that is largely unexplored for yield stress materials because of the difficulty describing the elastoviscoplastic behavior for arbitrary flows. Here, we measure the shear and extensional rheology of a simple tunable yield stress system: emulsions with different oil volume fractions that allow one to vary the flow properties over a large range. We propose universal concentration scaling laws that produce master curves for the shear and extensional rheology with a minimal number of known emulsion parameters. The extensional viscosity is obtained experimentally using a theory for inelastic shear-thinning materials, demonstrating that elastic stresses are unimportant in the pinching dynamics, and the elastic normal stress differences contribute minimally to the von Mises yield surface. Hence, this shows that material elasticity is unimportant, and an explicit constitutive equation of, for example, Criminale-Ericksen-Filby type, with a Herschel-Bulkley viscosity and a modulus equal to the Laplace pressure is adequate to describe the behavior of such concentrated soft-sphere systems in general steady and low Deborah number unsteady Eulerian and Lagrangian flows.