论文标题
衍生爱因斯坦有效粘度公式的轻度假设
Mild assumptions for the derivation of Einstein's effective viscosity formula
论文作者
论文摘要
我们为爱因斯坦公式提供了严格的推导，用于稀释悬架的有效粘度，$ n $刚性球，$ n \ gg 1 $，设置为尺寸$ 1 $的体积。到目前为止，大多数理由是在球之间的最小距离上进行的强烈假设：$ d_ {min} \ ge c n^{ - \ frac {1} {3}}} $，$ c> 0 $。我们将此假设放在一组弱弱的条件下放松：一个基本上表明球没有重叠，而另一个则可以控制彼此接近的球数。特别是，我们的分析涵盖了由标准泊松工艺建模的悬浮液的情况，几乎较小的硬核条件。
We provide a rigorous derivation of Einstein's formula for the effective viscosity of dilute suspensions of $n$ rigid balls, $n \gg 1$, set in a volume of size $1$. So far, most justifications were carried under a strong assumption on the minimal distance between the balls: $d_{min} \ge c n^{-\frac{1}{3}}$, $c > 0$. We relax this assumption into a set of two much weaker conditions: one expresses essentially that the balls do not overlap, while the other one gives a control of the number of balls that are close to one another. In particular, our analysis covers the case of suspensions modelled by standard Poisson processes with almost minimal hardcore condition.
