Transient Elasticity -- A Unifying Framework for Thixotropy, Polymers, and Granular Media

TL;DR

This paper introduces Transient Elasticity, a unified framework modeling thixotropic fluids, polymers, and granular media as transiently elastic systems with similar evolution equations, simplifying understanding of their complex behaviors.

Contribution

It proposes a simple, unified model based on transient elasticity that accounts for diverse non-Newtonian behaviors across different complex materials.

Findings

The model captures thixotropic effects that traditional viscous models cannot.

It demonstrates that thixotropic fluids behave elastically when fluidized.

The framework unifies the modeling of polymers, granular media, and yield stress fluids.

Abstract

Thixotropic yields stress fluids are complex materials such as paint, drilling mud, and food products like ketchup or yogurt. They behave as a solid below a certain shear stress (called yield stress), and flows as a liquid above it. The viscosity decreases over time and recovers when being at rest again. The usual picture is that a web of interacting particles exists at rest, which breaks down under stirring, shaking or shear rates, such that the system fluidizes into a viscous fluid with lumps. These decrease in size at higher rates, rendering the fluid less viscous. Back at rest, the lumps reconnect, re-establishing the web. In contrast, polymeric solutions have no yield stress, they always flow and deform elastically instead of breaking. The differences being clear-cut, these are two distinct systems, to be emulated by very different models. This paper presents an alternative picture: When fluidized, structural destruction is not complete, and sufficient connections are left intact, rendering thixotropic yield stress fluids transiently elastic, such that they behave viscous if stationary, with little evidence of recoverable elastic strain, but it is elasticity that underlines its non-Newtonian behavior, not a complex viscosity. They obey the same evolution equations as polymers, differing only in their parameters. With this idea, it turns out quite simple to account for a wide range of thixotropic effects, including some that fail to fit the viscous picture. More technically, starting from solid-dynamics and letting the elastic strain relax, interpolates between solid- and fluid-dynamics. Realizing in addition that complex systems such as structured fluids often sustain two temperatures, yields a nonlinear model called Transient Elasticity (TE). Its adequacy for polymers and granular media was shown in previous papers. Here, it is applied to thixotropic yield-stress fluids.