论文标题
通过均质化，非球形布朗刚性颗粒引起的粘弹性应力的衍生作用
Derivation of the viscoelastic stress in Stokes flows induced by non-spherical Brownian rigid particles through homogenization
论文作者
论文摘要
我们考虑了$ n $相同的轴对称性刚性的刚性布朗颗粒的微观模型。我们严格地衍生出许多小粒子的均质化极限，是粘弹性应力的经典公式，该公式出现在所谓的doi模型中，这些模型将fokker-planck方程与stokes方程搭配。我们认为deborah的订单数量为$ 1 $和很小的Deborah数字。我们的微观模型包含几种简化，最重要的是，我们忽略了粒子中心的时间演变以及用于粒子方向演变的流体动力相互作用。在Stratonovitch噪声方面，微观流体速度是由颗粒处的torques的Stokes方程建模的。我们从无限的尺寸Stratonovitch积分方面给出了该PDE的含义。这需要分析穿孔域中Stokes方程的形状衍生物，我们通过反射方法来完成。
We consider a microscopic model of $n$ identical axis-symmetric rigid Brownian particles suspended in a Stokes flow. We rigorously derive in the homogenization limit of many small particles a classical formula for the viscoelastic stress that appears in so-called Doi models which couple a Fokker-Planck equation to the Stokes equations. We consider both Deborah numbers of order $1$ and very small Deborah numbers. Our microscopic model contains several simplifications, most importantly, we neglect the time evolution of the particle centers as well as hydrodynamic interaction for the evolution of the particle orientations. The microscopic fluid velocity is modeled by the Stokes equations with given torques at the particles in terms of Stratonovitch noise. We give a meaning to this PDE in terms of an infinite dimensional Stratonovitch integral. This requires the analysis of the shape derivatives of the Stokes equations in perforated domains, which we accomplish by the method of reflections.
