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Integral modeling and reinforcement learning control of three-dimensional liquid metal coating on a moving substrate

Fabio Pino1,2,*,†, Edoardo Fracchia1,3,‡, Benoit Scheid2, and Miguel A. Mendez1,4,5

  • *Contact author: fp448@cam.ac.uk
  • †Present address: Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Cambridge, United Kingdom.
  • ‡Present address: Currently at Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, Italy.
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Phys. Rev. Fluids 11, 044003 – Published 28 April, 2026

DOI: https://doi.org/10.1103/77zf-ks57

Abstract

Metallic coatings are used to enhance the durability of metal surfaces by protecting them from corrosion. These protective layers are typically deposited in a fluid state via a liquid film. Controlling instabilities in the liquid film is crucial to achieving uniform, high-quality coatings. This study explores the possibility of controlling liquid films on a moving substrate using a combination of gas jets and electromagnetic actuators. To model the three-dimensional liquid film, we extend existing integral models to incorporate the effects of electromagnetic actuators. The control strategy was developed within a reinforcement learning framework, in which the proximal policy optimization (PPO) algorithm interacts with the liquid film via pneumatic and electromagnetic actuators to optimize a reward function that accounts for instability-wave amplitude through a trial-and-error process. The PPO identified an optimal control law that reduced interface instabilities via a novel mechanism: gas jets push crests, and electromagnets raise troughs via the Lorentz force.

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Outline

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Phys. Rev. Fluids 11, 044003– Published 28 April, 2026
  • Received 18 March 2025
  • Accepted 23 January 2026
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