论文标题
随机悬浮液的沉积和超均匀性的影响
Sedimentation of random suspensions and the effect of hyperuniformity
论文作者
论文摘要
这项工作涉及对粘性流体重力下定居的刚性颗粒随机悬浮液的数学分析。每个粒子都会产生一个流体流，进而作用于其他颗粒并阻碍其沉降。从平衡的角度来看，对于给定的粒子位置集合，我们分析了相关的平均沉降速度和单个颗粒的速度波动。在1970年代，基于远程粒子贡献的适当重质化，Batchelor对平均沉降速度（在物理学上是一个60岁的开放式问题）进行了适当的定义。在1980年代，Caflisch和Luke的著名正式计算表明，尺寸的速度波动$ d = 3 $应该与沉积罐的大小相反，与直觉和实验性观察相矛盾。后来提出了对悬浮颗粒的远程自组织以悬浮颗粒的形式的作用，以解释稳态观察中这种差异的额外筛选。在目前的贡献中，我们开发了第一个严格的理论，该理论允许证明物理文献的所有正式计算是合理的。
This work is concerned with the mathematical analysis of the bulk rheology of random suspensions of rigid particles settling under gravity in viscous fluids. Each particle generates a fluid flow that in turn acts on other particles and hinders their settling. In an equilibrium perspective, for a given ensemble of particle positions, we analyze both the associated mean settling speed and the velocity fluctuations of individual particles. In the 1970s, Batchelor gave a proper definition of the mean settling speed, a 60-year-old open problem in physics, based on the appropriate renormalization of long-range particle contributions. In the 1980s, a celebrated formal calculation by Caflisch and Luke suggested that velocity fluctuations in dimension $d=3$ should diverge with the size of the sedimentation tank, contradicting both intuition and experimental observations. The role of long-range self-organization of suspended particles in form of hyperuniformity was later put forward to explain additional screening of this divergence in steady-state observations. In the present contribution, we develop the first rigorous theory that allows to justify all these formal calculations of the physics literature.
