Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting and transport. This paper studies a class of mean field control formulations for these droplet dynamics, which can be used to control and manipulate droplets in applications. We first formulate the droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. We then design an optimal control problem for these gradient flows. As an example, a lubrication equation for a thin volatile liquid film laden with an active suspension is developed, with control achieved through its activity field. Lastly, we apply the primal–dual hybrid gradient algorithm with high-order finite-element methods to simulate the proposed mean field control problems. Numerical examples, including droplet formation, bead-up/spreading, transport, and merging/splitting on a two-dimensional spatial domain, demonstrate the effectiveness of the proposed mean field control mechanism.
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Droplet impact on liquid films: Bouncing-to-merging transitions for two-liquid systems
The dynamics of a liquid droplet impacting a liquid film of different compositions is critical for many industrial processes, including additive manufacturing and bio-printing. In this work we present an exposition of droplet impact on liquid films investigating the effects of mismatch in their properties on bouncing-to-merging transitions. Experiments are conducted for two sets of liquid combinations, namely, alkanes and silicon oils. The regime maps for impact outcomes (bouncing vs merging) are created from detailed experiments with various single- and two-liquid systems. The results highlight that the two-liquid systems exhibit an additional merging regime, which is not observed for single-liquid systems. Subsequently, the scaling analyses for transitional boundaries between various regimes are revisited, and new scaling laws are proposed to include the effects of asymmetry in the droplet and film properties. Finally, the experimental results are used to assess the performance of the proposed scaling laws.
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- Award ID(s):
- 2145210
- PAR ID:
- 10391221
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 34
- Issue:
- 10
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 103313
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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