Investigating and Modeling the Rheology and Flow Instabilities of Thixotropic Yield Stress Fluids

Abstract

Many complex fluids exhibit thixotropy – their viscosity, moduli, and yield stress gradually decrease under flow and slowly build up after the cessation of flow. Thixotropic fluids are very common in nature and industry. Examples include colloidal suspensions, gels, paints, pastes, crude oils, adhesives, personal care products, and many food materials. A thorough understanding of their rheological properties and flow behaviors is very important in the product development, process flow simulation, and product quality control of those materials. The goal of this thesis is to advance the understanding of the rheology and flow instability of thixotropic fluids.

Thixotropy often occurs simultaneously with other rheological phenomena such as yielding, viscoelasticity, and aging, which poses a great challenge in both experimental and theoretical studies. We first focus on the “ideal,” purely viscous, thixotropic response, which dominates for shear histories involving only relatively high shear rates. We show that to predict quantitatively an ideal thixotropic response, it is critical to introduce multiple timescales for thixotropic evolution and use nonlinear kinetic equations. We propose a novel “multi-lambda” (ML) model that introduces a spectrum of timescales at the cost of only one additional model parameter. We examine this model against a wide range of shear-rate histories involving steady state, step shear rate, step stress, shear rate ramp, and stress ramp. The model shows quantitative predictions of the experimental data.

We next generalize the ML model and combine it with an isotropic kinematic hardening (IKH) model to predict complex thixotropic elasto-viscoplastic (TEVP) responses. We evaluate this new model and compare its predictions with three representative TEVP models over a wide range of test conditions. We also provide a tensorial formulation of the ML-IKH model that is frame-invariant, obeys the second law of thermodynamics, and can reproduce the quantitative predictions of the scalar version.

Shear banding often occurs in complex fluids, which greatly alters the local flow fields and hence the bulk rheological response. Understanding this phenomenon is crucial to interpret the rheological data correctly and is important in the design of processing flows that enhance or mitigate it as needed. Nevertheless, it has been unclear how shear bands occur and evolve in thixotropic fluids. We design a novel particle image velocimetry method to study the banding dynamics in a thixotropic fumed silica suspension under transient shear. We find that in shear startup experiments, the material exhibits a critical shear rate at around 0.2 s−1, below which shear bands can occur. The banding dynamics show a strong dependence on shear strain – the flow remains uniform for strain smaller than unity and bands quickly grow when the strain exceeds unity. Upon a sudden reversal of the shearing direction, shear bands show a non-monotonic evolution – shear bands grow slightly for strain less than 0.15, then gradually homogenize until the strain reaches around 1.5, after which bands slowly grow. We propose a simple thixotropic kinematic hardening model that can qualitatively capture the main features of the banding dynamics.