A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic fluid

TL;DR

This paper introduces a nonlinear dynamical system model that effectively predicts the yielding behavior of viscoplastic fluids, aligning well with microscopic simulations and experimental observations, and capturing key transition features with minimal parameters.

Contribution

The paper presents a novel nonlinear dynamical system model with only two parameters that accurately describes the solid-fluid transition in viscoplastic materials.

Findings

Model aligns with microscopic simulations

Captures hysteresis and transition abruptness

Consistent with experimental scaling laws

Abstract

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stress recently reported in [1] is presented. The predictions of the model are in a fair agreement with the microscopic simulations and in a very good agreement with the microstructural semi-empirical model reported in [2]. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forcing.The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations.