论文标题
施加在两个相邻$ m $ -convex颗粒上的流体动力的爆炸分析
Blow-up analysis of hydrodynamic forces exerted on two adjacent $M$-convex particles
论文作者
论文摘要
在粘性不可压缩的流体中，在两个相对运动的近距离刚性颗粒上作用的流体动力总是任意变大，因为粒子间距离参数$ \ varepsilon $变为零。在本文中，我们以$ 2 \ mathrm {d} $模型获得了流体动力和扭矩的渐近公式，并在$ 3 \ mathrm {d} $中建立了最佳的上和下限估计，这急剧表征了流体动力的奇异行为。这些结果揭示了粒子之间的相对凸度，用指数$ m $表示，对流体动力的爆炸率。此外，当$ m $变成无穷大时，我们考虑具有部分平坦边界的粒子，并捕获了水动力力的最大爆炸速率为$ \ varepsilon^{ - 3} $均在2D和3D中。我们还阐明了线性运动和旋转运动引起的奇异性，并发现旋转引起的最大爆炸速率出现在力的所有方向上。
In a viscous incompressible fluid, the hydrodynamic forces acting on two close-to-touch rigid particles in relative motion always become arbitrarily large, as the interparticle distance parameter $\varepsilon$ goes to zero. In this paper we obtain asymptotic formulas of the hydrodynamic forces and torque in $2\mathrm{D}$ model and establish the optimal upper and lower bound estimates in $3\mathrm{D}$, which sharply characterizes the singular behavior of hydrodynamic forces. These results reveal the effect of the relative convexity between particles, denoted by index $m$, on the blow-up rates of hydrodynamic forces. Further, when $m$ degenerates to infinity, we consider the particles with partially flat boundary and capture that the largest blow-up rate of the hydrodynamic forces is $\varepsilon^{-3}$ both in 2D and 3D. We also clarify the singularities arising from linear motion and rotational motion, and find that the largest blow-up rate induced by rotation appears in all directions of the forces.
