Numerical simulations of a sphere settling in simple shear flows of yield stress fluids

TL;DR

This study uses 3D numerical simulations to explore how a sphere's sedimentation in yield stress fluids is affected by simple shear flows, revealing drag reduction and flow asymmetry changes due to elasticity and shear effects.

Contribution

It introduces a coupled elastovisco-plastic model with immersed boundary method to analyze sphere sedimentation under shear in yield stress fluids, highlighting nonlinear flow interactions.

Findings

Drag on the sphere is significantly reduced by shear flow.

Negative wake disappears with applied shear flow.

Drag cannot be predicted by pure sedimentation laws in sheared conditions.

Abstract

We perform $3$D numerical simulations to investigate the sedimentation of a single sphere in the absence and presence of a simple cross shear flow in a yield stress fluid with weak inertia. In our simulations, the settling flow is considered to be the primary flow, whereas the linear cross shear flow is a secondary flow with amplitude $10\%$ of the primary flow. To study the effects of elasticity and plasticity of the carrying fluid on the sphere drag as well as the flow dynamics, the fluid is modeled using the elastovisco-plastic (EVP) constitutive laws proposed by \cite{saramito2009new}. The extra non-Newtonian stress tensor is fully coupled with the flow equation and the solid particle is represented by an immersed boundary (IB) method. Our results show that the fore-aft asymmetry in the velocity is less pronounced and the negative wake disappears when a linear cross shear flow is applied. We find that the drag on a sphere settling in a sheared yield stress fluid is reduced significantly as compared to an otherwise quiescent fluid. More importantly, the sphere drag in the presence of a secondary cross shear flow cannot be derived from the pure sedimentation drag law owing to the non-linear coupling between the simple shear flow and the uniform flow. Finally, we show that the drag on the sphere settling in a sheared yield-stress fluid is reduced at higher material elasticity mainly due to the form and viscous drag reduction.