Wilczek Markus, Tewes Walter, Engelnkemper Sebastian, Gurevich Svetlana V, Thiele Uwe
Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, D-48149 Münster, Germany.
Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, D-48149 Münster, Germany.
Phys Rev Lett. 2017 Nov 17;119(20):204501. doi: 10.1103/PhysRevLett.119.204501. Epub 2017 Nov 14.
Ensembles of interacting drops that slide down an inclined plate show a dramatically different coarsening behavior as compared to drops on a horizontal plate: As drops of different size slide at different velocities, frequent collisions result in fast coalescence. However, above a certain size individual sliding drops are unstable and break up into smaller drops. Therefore, the long-time dynamics of a large drop ensemble is governed by a balance of merging and splitting. We employ a long-wave film height evolution equation and determine the dynamics of the drop size distribution towards a stationary state from direct numerical simulations on large domains. The main features of the distribution are then related to the bifurcation diagram of individual drops obtained by numerical path continuation. The gained knowledge allows us to develop a Smoluchowski-type statistical model for the ensemble dynamics that well compares to full direct simulations.
与水平板上的液滴相比，沿倾斜板下滑的相互作用液滴集合表现出截然不同的粗化行为：由于不同大小的液滴以不同速度下滑，频繁碰撞导致快速聚结。然而，超过一定尺寸后，单个下滑液滴不稳定并破碎成更小的液滴。因此，大液滴集合的长期动力学受合并和分裂平衡的支配。我们采用长波薄膜高度演化方程，并通过在大区域上的直接数值模拟确定液滴尺寸分布向稳态的动力学。然后将分布的主要特征与通过数值路径延拓获得的单个液滴的分岔图相关联。所获得的知识使我们能够为集合动力学开发一个与完整直接模拟非常匹配的斯莫卢霍夫斯基型统计模型。
