论文标题
用于随机悬浮液的Batchelor-Green公式的推导
Derivation of Batchelor-Green formula for random suspensions
论文作者
论文摘要
本文专用于无惯性的悬浮液的有效粘度，在低实量分数$ ϕ $下。目的是严格地得出有效粘度的$ O（ϕ^2）$公式。在以前的作品中，为刚性球提供了这样的公式，满足了强大的分离假设$ d_ {min} \ ge c cϕ^{ - \ frac13} r $，其中$ d_ {min} $是球形和$ r $ radius之间的最小距离。然后将其应用于具有分离的周期性和随机配置，以获得$ O（ϕ^2）$系数的明确值。我们在这里考虑互补（肯定是更现实的）随机配置，满足了分离和远程去相关的软假设。我们在这种著名的batchelor-green公式中证明是合理的。例如，我们的结果适用于几乎最小的硬核假设$ d_ {min}>（2+ε）r $，$ε> 0 $的硬核泊松点过程。
This paper is dedicated to the effective viscosity of suspensions without inertia, at low solid volume fraction $ϕ$. The goal is to derive rigorously a $o(ϕ^2)$ formula for the effective viscosity. In previous works, such formula was given for rigid spheres satisfying the strong separation assumption $ d_{min} \ge c ϕ^{-\frac13} r$, where $d_{min}$ is the minimal distance between the spheres and $r$ their radius. It was then applied to both periodic and random configurations with separation, to yield explicit values for the $O(ϕ^2)$ coefficient. We consider here complementary (and certainly more realistic) random configurations, satisfying soft assumptions of separation and long range decorrelation. We justify in this setting the famous Batchelor-Green formula. Our result applies for instance to hardcore Poisson point process with almost minimal hardcore assumption $d_{min} > (2+ε) r$, $ε> 0$.
