A constitutive equation for thixotropic suspensions with yield stress by coarse‐graining a population balance model

Abstract

A population balance model appropriate for the shear flow of thixotropic colloidal suspensions with yield stress is derived and tested against experimental data on a model system available in the literature. Modifications are made to account for dynamic arrest at the onset of the yield stress, in addition to enforcing a minimum particle size below which breakage is not feasible. The resulting constitutive model also incorporates a structural based relaxation time, unlike existing phenomenological models that use the inverse of the material shear rate as the relaxation time. The model provides a reasonable representation of experimental data for a model thixotropic suspension in the literature, capturing the important thixotropic timescales. When compared to prevalent structure kinetics models, the coarse‐grained population balance equation is shown to be distinct, emphasizing the novelty of utilizing population balances as a basis for thixotropic suspension modeling. © 2016 American Institute of Chemical Engineers AIChE J, 63: 517–531, 2017