Year: 2024
Type: article
Abstract: 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.
Source: Journal of Fluid Mechanics
DOI: 10.1017/jfm.2024.983
Authors: Guosheng Fu, Hangjie Ji, Will Pazner, Wuchen Li
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, Algorithms, Theory, and Applications for Fiber Coating Systems, FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems, G2723991902, G4369523871, RTG: Program in Computation- and Data-Enabled Science, Collaborative Research: Energetic Variation Based Numerical Studies in Complex Fluids with Thermo-Chemo-Mechanical Effects, RTG: Mathematical Foundation of Data Science at University of South Carolina
OpenAlex ID: W4404547037