Viscoelastic response of impact process on dense suspensions

Abstract

We numerically study impact processes on dense suspensions using the lattice Boltzmann method to elucidate the connection between the elastic rebound of an impactor and relations among the impact speed u0, maximum force acting on the impactor Fmax, and elapsed time tmax to reach Fmax. We find that tmax emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of Fmax from the u0 independent regime for low u0 to a power law regime satisfying Fmax∝u0α with α≈1.5 for high u0. Similarly, tmax satisfies tmax∝u0β with β≈−0.5 for high u0. Both power-law relations for Fmax and tmax vs u0 for high u0 are independent of the system size, but the rebound phenomenon strongly depends on the depth of the container for suspensions. Thus, we indicate that the rebound phenomenon is not directly related to the relations among u0, Fmax and tmax. We propose a floating + force chain model, where the rebound process is caused by an elastic term that is proportional to the number of the connected force chains from the impactor to the bottom plate. On the other hand, there are no elastic contributions in the relations for Fmax and tmax against u0 because of the absence of percolated force chains in the early stage. This phenomenology predicts Fmax∝u03/2 and tmax∝u0−1/2 for high u0 and also recovers the behavior of the impactor quantitatively even if there is the rebound process.