Optimal electrostatic control and reduced-order modelling of thick-film flow on a uniformly rotating cylinder

The dynamics of a thick, two-dimensional film of a perfectly conducting, Newtonian fluid coating a uniformly rotating, horizontal, circular cylinder are studied. The cylinder is held at a constant potential and a concentric outer electrode encloses the system, inducing electrostatic forces at the fluid-gas interface. The potential at the outer electrode is, in general, non-uniform, and can be used as a control actuation mechanism. Long-wave scalings¹ are used along with the Method of Weighted Residuals² to derive a model that is valid for both thin and thick films, and incorporates the effects of electrostatic stress, rotation, gravity, viscosity, inertia, and capillarity. Optimal control theory is applied to the model to explore the possibilities of controlling the dynamics of the film using the induced electric field.

¹ Wray, A. W. and Cimpeanu, R. (2020). Reduced-order modelling of thick inertial flows around rotating cylinders. J. Fluid Mech., 898, A1.

² Ruyer-Quil, C. and Manneville, P. (2000). Improved modeling of flows down inclined planes. Eur. Phys. J. B, 15 (2), 357–369.