论文标题
滴在斯托克斯流中的沉积
On the sedimentation of a droplet in Stokes flow
论文作者
论文摘要
本文致力于对介质模型的分析，该模型描述了介质缩放下粘性流中惯性悬浮液的沉积。该论文分为两个部分，第一部分涉及对运输stokes模型的分析，其中包括全球存在和唯一性结果，$ l^1 \ cap l^\ infty $初始密度具有有限的第一刻。我们特别研究了初始条件是单位球的特征函数，并表明我们恢复了hadamard-rybczynski结果，即液滴的球形形状在时间上保存。在本文的第二部分中，我们在液滴的初始形状为轴对称的情况下得出了表面演化模型。我们获得了一个一维双曲方程，包括与Stokes方程的奇异绿色函数相关的非本地运算符。我们提出局部存在和独特性结果，并表明我们恢复了Hadamard-rybczynski的结果，只要建模得到很好的定义并在球形案例中用数值模拟完成。
This paper is dedicated to the analysis of a mesoscopic model which describes sedimentation of inertialess suspensions in a viscous flow at mesoscopic scaling. The paper is divided into two parts, the first part concerns the analysis of the transport-Stokes model including a global existence and uniqueness result for $L^1\cap L^\infty$ initial densities with finite first moment. We investigate in particular the case where the initial condition is the characteristic function of the unit ball and show that we recover Hadamard-Rybczynski result, that is, the spherical shape of the droplet is preserved in time. In the second part of this paper, we derive a surface evolution model in the case where the initial shape of the droplet is axisymmetric. We obtain a 1D hyperbolic equation including non local operators that are linked to the convolution formula with respect to the singular Green function of the Stokes equation. We present a local existence and uniqueness result and show that we recover the Hadamard-Rybczynski result as long as the modelling is well defined and finish with numerical simulations in the spherical case.
