Fully-resolved simulations of a sphere settling in an initially unstructured thixo-viscoplastic fluid

Abstract

This paper investigates the settling of a single spherical particle immersed in an initially unstructured thixo-viscoplastic fluid. The phenomenon was numerically solved using the lattice Boltzmann method (LBM) for the mass and momentum transport equations, the immersed boundary method (IBM) for the particle dynamics, and the advection-diffusion LBM for the structural parameter transport equation. We utilized a simplified version of the Houska model to represent the rheological behavior of an inelastic thixo-viscoplastic material. The model evaluates the yield stress effects, which change based on a structural parameter, in the particle settling of an aging fluid. We fixed the particle properties (diameter, density) and varied the fluid rheological properties, such as the static and dynamic Bingham numbers and the build-up and breakdown numbers. Detailed fields of velocity, rate-of-strain, and structural parameters are presented to enrich the flow interpretation. The numerical results reveal that, for a thixotropic fluid, the classical viscoplastic critical yield number criterion does not correctly predict the condition for which the particle will become stationary. Although a higher dynamic yield stress will help the particle's stoppage, the microstructural breakdown has a powerful effect in facilitating its settling.