Morton M. Denn

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.

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, with an intermediate region of stress in which the material is flowable.

Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to, or even larger than, the shear stress. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting nonviscometric flow behavior. Very little attention has thus far been paid to the normal stresses of yield stress fluids, which are difficult to measure. We report the first systematic study of the first and second normal stress differences in both continuous and slow oscillatory shear of three model nonthixotropic yield stress fluids, with N1 > 0 and N2 < 0. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress. However, the contribution of the normal stresses to the von Mises yield criterion for these materials is small.

Here, we provide an overview of our understanding of shear thickening and the methods that have been developed to describe it, as well as outstanding questions.

EPJ Web of Conferences, open-access proceedings in physics and astronomy