Electrostatic control of the Navier-Stokes equations for thin films

TL;DR

This paper presents a control scheme for thin film flows governed by Navier-Stokes equations, utilizing electrostatic forces via electrodes to manipulate the interface shape and other flow characteristics.

Contribution

It introduces a novel electrostatic control method combining model predictive and optimal control for multiphase thin film flows.

Findings

Successful control of the interfacial shape of the fluid

Demonstrated robustness of the control scheme

Applicable to controlling various flow quantities

Abstract

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.