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Sliding Drops: Ensemble Statistics from Single Drop Bifurcations

Markus Wilczek, Walter Tewes, Sebastian Engelnkemper, Svetlana V. Gurevich, and Uwe Thiele
Phys. Rev. Lett. 119, 204501 – Published 14 November 2017
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Abstract

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.

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  • Received 2 June 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.204501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsFluid Dynamics

Authors & Affiliations

Markus Wilczek1,2,*, Walter Tewes1, Sebastian Engelnkemper1, Svetlana V. Gurevich1,2,3, and Uwe Thiele1,2,3,†

  • 1Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Strasse 9, D-48149 Münster, Germany
  • 2Center for Nonlinear Science (CeNoS), University of Münster, Corrensstrasse 2, D-48149 Münster, Germany
  • 3Center for Multiscale Theory and Computation (CMTC), University of Münster, Corrensstrasse 40, D-48149 Münster, Germany

  • *markuswilczek@uni-muenster.de
  • u.thiele@uni-muenster.de

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Issue

Vol. 119, Iss. 20 — 17 November 2017

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