Electrostatic control of the Navier-Stokes equations for thin films

Wray, Alexander W. and Cimpeanu, Radu and Gomes, Susana (2022) Electrostatic control of the Navier-Stokes equations for thin films. Physical Review Fluids, 7 (12). L122001. ISSN 2469-990X (https://doi.org/10.1103/PhysRevFluids.7.L122001)

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A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate, which induces an electric field in the gas phase, and a resultant Maxwell stress at the liquid-gas interface. The imposed potential at the second electrode is derived using a model predictive control loop, together with optimal control of a high-fidelity reduced-dimensional model. In this implementation the interfacial shape of the fluid is successfully controlled; however, the algorithm is sufficiently general to control any other quantity of interest.