arXiv 2106.134042021-06cond-mat.soft

稠密悬浮体冲击过程的粘弹性响应

Viscoelastic response of impact process on dense suspensions

Pradipto, Hisao Hayakawa

发表信息：: Physics of Fluids 33, 093110 (2021)
DOI：: 10.1063/5.0112193

摘要：

本文用格子玻尔兹曼方法数值研究了稠密悬浮液的撞击过程，阐明了撞击体的弹性回弹与撞击速度$u_0$、撞击体上的最大力$F_{\rm max}$和到达$F_{\rm max}$所需时间$t_{\rm max}$之间的关系。研究发现，$t_{\rm max}$出现在冲击的早期，而反弹过程发生在冲击的后期。我们发现$F_{\rm max}$从低$u_0$的$u_0$独立机制到高$u_0$的满足$F_{\rm max}\propto u_0^α$和$α\approx 1.5$的幂律机制的交叉。类似地，对于高$u_0$，$t_{\rm max}$满足$t_{\rm max}\propto u_0^β$和$β\approx -0.5$。对于高$u_0$，$F_{\rm max}$和$t_{\rm max}$与$u_0$的幂律关系与系统尺寸无关，但回弹现象强烈依赖于悬浮液容器的深度。因此，我们指出，反弹现象是没有直接关系的$u_0$，$F_{\rm max}$和$t_{\rm max}$之间的关系。我们提出了一个浮动+力链模型，其中的反弹过程是由一个弹性项，这是成比例的数量连接的力链从冲击器的底板。另一方面，由于在早期阶段不存在压缩力链，因此在$F_{\rm max}$和$t_{\rm max}$对$u_0$的关系中没有弹性贡献。该现象学预测了高$u_0$的$F_{\rm max}\propto u_0^{3/2}$和$t_{\rm max}\propto u_0^{-1/2}$，并且即使存在回弹过程，也定量地恢复了撞击器的行为。

英文摘要：

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 $u_0$, maximum force acting on the impactor $F_{\rm max}$, and elapsed time $t_{\rm max}$ to reach $F_{\rm max}$. We find that $t_{\rm max}$ emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of $F_{\rm max}$ from $u_0$ independent regime for low $u_0$ to a power law regime satisfying $F_{\rm max}\propto u_0^α$ with $α\approx 1.5$ for high $u_0$. Similarly, $t_{\rm max}$ satisfies $t_{\rm max}\propto u_0^β$ with $β\approx -0.5$ for high $u_0$. Both power-law relations for $F_{\rm max}$ and $t_{\rm max}$ versus $u_0$ for high $u_0$ 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 $u_0$, $F_{\rm max}$ and $t_{\rm max}$. 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 $F_{\rm max}$ and $t_{\rm max}$ against $u_0$ because of the absence of percolated force chains in the early stage. This phenomenology predicts $F_{\rm max}\propto u_0^{3/2}$ and $t_{\rm max}\propto u_0^{-1/2}$ for high $u_0$ and also recovers the behavior of the impactor quantitatively even if there is the rebound process.

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英文摘要：

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