Effective viscosity and elasticity in dense suspensions under impact: Toward a modeling of walking on suspensions

TL;DR

This paper investigates the elastic response of dense suspensions under impact using coupled simulation methods and proposes a reduced model that captures impactor dynamics, including walking-like bouncing behavior, with insights into parameter effects.

Contribution

It introduces a reduced model for impactor motion in dense suspensions, validated against detailed simulations, and applies it to analyze walking-like bouncing behavior.

Findings

Elastic forces exist without percolating clusters.

The reduced model accurately predicts impactor dynamics.

Spring stiffness influences bouncing behavior.

Abstract

The elastic response of dense suspensions under an impact is studied using coupled Lattice Boltzmann Method and Discrete Element Method (LBM-DEM) and its reduced model. We succeed to extract the elastic force acting on the impactor in dense suspensions, which can exist even in the absence of percolating clusters of suspended particles. We then propose a reduced model to describe the motion of the impactor and demonstrate its relevancy through the comparison of the solution of the reduced model and that of LBM-DEM. Furthermore, we illustrate that the perturbation analysis of the reduced model captures the short-time behavior of the impactor motion quantitatively. We apply this reduced model to the impact of the foot-spring-body system on a dense suspension, which is the minimal model to realize walking on the suspension. Due to the spring force of the system and the stiffness of the suspension, the foot undergoes multiple bounces. We also study the parameter dependencies of the hopping motion and find that multiple bounces are suppressed as the spring stiffness increases.