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Sliding Drops: Ensemble Statistics from Single Drop Bifurcations.

Markus Wilczek1,2, Walter Tewes1, Sebastian Engelnkemper1

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Summary
This summary is machine-generated.

Sliding drops on inclined plates merge and split, unlike stationary drops. This study models the complex dynamics of drop size distribution, revealing a balance between coalescence and breakup for sliding fluid ensembles.

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Area of Science:

  • Fluid dynamics
  • Complex systems
  • Surface science

Background:

  • Drops on horizontal surfaces exhibit coarsening via coalescence.
  • Sliding drops on inclined plates present unique dynamics due to velocity differences and instability.

Purpose of the Study:

  • To investigate the coarsening behavior of interacting sliding drops on an inclined plate.
  • To model the drop size distribution dynamics and understand the balance between merging and splitting.

Main Methods:

  • Utilized a long-wave film height evolution equation.
  • Performed direct numerical simulations on large domains to analyze drop ensemble dynamics.
  • Employed numerical path continuation to study individual drop bifurcation diagrams.

Main Results:

  • Observed that sliding drops undergo both coalescence and breakup, unlike stationary drops.
  • Determined the dynamics of drop size distribution approaching a stationary state.
  • Developed a Smoluchowski-type statistical model that accurately predicts ensemble dynamics.

Conclusions:

  • The long-time dynamics of sliding drop ensembles are governed by a balance between merging (coalescence) and splitting (breakup).
  • The developed statistical model effectively captures the complex behavior of these fluid systems.