Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids

Abstract

In this study, we present a homogenization model for the macroscopic rheological behavior of non-colloidal suspensions of initially spherical, viscoelastic particles in yield stress fluids, which are subjected to uniform flow conditions. The constitutive behavior of the suspending fluid is characterized by the Herschel-Bulkley (HB) model, and the particles are assumed to be neutrally buoyant solids characterized by the finite-strain Kelvin-Voigt viscoelastic behavior. We make use of the "linear comparison composite" variational technique of Ponte Castañeda (J. Mech. Phys. Solids, vol 39, 1991, pp. 45-71) to approximate the instantaneous response of the suspensions of viscoelastic particles in the HB fluid by that of a fictitious suspension consisting of the same particles distributed identically in a Newtonian fluid with a suitably-chosen viscosity. The response of the latter suspension is then estimated by the homogenization model, recently developed by Avazmohammadi and Ponte Castañeda (J. Fluid Mech., vol 763, 2015, pp. 386-432), which, when combined with appropriate evolution laws for the relevant microstructural variables, provides a complete characterization of the time-dependent response of the actual suspensions. With the objective of illustrating the key features of our model, we consider the particular case of suspensions of elastic particles in HB fluids under shear flow conditions. The results provide a broad picture of the influence of the HB fluid and * Corresponding author, particle constitutive properties, as well as of the particle volume fraction on the effective time-dependent and steady-state behaviors of the suspensions. For the special case of non-deformable particles, our model predicts that the suspensions behave like HB fluids with modified properties, consistent with the results of Chateau et al. (J.D Strain-rate tensor [1/s] D eq Equivalent strain-rate [1/s] J m Particle strain-locking parameter [-] K Fluid consistency constant [Ns n /m 2 ] n Fluid power-law index [-] t Time [s]

Pair-particle trajectories in a shear flow of a Bingham fluid

“…Since yield stress fluids are used in the industry to stabilize the particles against gravity, the sedimentation problem has been the subject of most studies on particles suspended in yield stress fluids [4,22,46,53] , with a focus on a single particle and on the onset of flow. The rheological properties of model suspensions have also been studied recently experimentally [13,39,45] and theoretically [3,8] . The method used by Chateau et al [8] , valid for any generalized Newtonian behavior, consists, first, in assuming that the overall properties of the suspension can be accurately estimated from an average estimate ̄̇l ocal of the local shear rate over the suspending fluid domain, second, in using one of the material properties determined experimentally to estimate the value of ̄̇l ocal , and finally, in using this last value to predict the other properties.…”

Effects of Polydispersity on Structuring and Rheology in Flowing Suspensions

“…A potential alternate approach for the future is to use homogenization methods, e.g. [55][56][57][58][59] that have also been used to similar ends. While these have the important advantage that non-Newtonian systems can tractably be solved numerically, they do not track individual bubbles / particles.…”

Surfactant stabilized bubbles flowing in a Newtonian fluid

“…Homogenization or mixture-theory based approaches, e.g. based on [4,[45][46][47][48][49][50][51][52][53], may enable the formulation of continuum models that can provide insight into particle structuring while also accounting for the complex rheology of cement paste.…”