Zahnow Jens C, Vilela Rafael D, Feudel Ulrike, Tél Tamás
Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):055301. doi: 10.1103/PhysRevE.77.055301. Epub 2008 May 6.
Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in raindrop statistics and in stirring tank experiments.
在混沌流中平流的惯性粒子通常会聚集在奇怪吸引子中。在这些分形集中移动时，它们通常会相互靠近并碰撞。在此，我们考虑碰撞时聚集的惯性粒子。在此过程中形成的新粒子更大，并遵循带有新参数的运动方程。当这些粒子达到一定尺寸或剪切力变得足够大时，它们又会破碎。由此产生的系统由大量共存的具有不同粒子数的动态系统组成。我们发现聚集和破碎的结合会导致渐近稳态。渐近粒子尺寸分布取决于破碎机制。该模型产生的尺寸分布与雨滴统计和搅拌槽实验中发现的分布一致。
