Thin layers of liquids, known as liquid films, are found in numerous contexts in both nature and industry. A common example is water flowing down a windscreen on a rainy day. Liquid films are ubiquitous in technological applications, such as the manufacture of LCD screens and liquid-based cooling systems for large-scale computing systems. Irrespective of the context, the ability to control the shape of liquid films is critical, be it towards flattening the film to achieve defect-free coatings, or towards achieving larger contact area for better removal of heat.

Radu CimpeanuLink opens in a new window and Susana GomesLink opens in a new window work to understand liquid films mathematically by bringing together modelling, asymptotic analysis, control theory and computational fluid dynamics in new and exciting ways – "we derive novel partial differential equation-based evolution equations that are simplified models (compared to the full description of liquid films) capable of efficiently describing the often highly nonlinear fluid flow."

Controlling liquid films can be achieved through many physical approaches: blowing and suction of fluid through slots, applying electric fields, or applying thermal actuation. Models developed at Warwick act as an invaluable testbed for control methods where the interplay between observations and control action is the key to successful control. Most importantly, simplified mathematical models allow researchers to obtain tractable analytical results that underpin general control strategies. Such control strategies have then been successfully usedLink opens in a new window in conjunction with much more expensive direct numerical simulations. (High-accuracy direct numerical simulations with few simplifications are our closest equivalent to a real-world experiment, but they often require thousands of CPU hours each and hence they are poor exploratory tools on their own.) Simplified mathematical models can provide valuable insight and more readily identify the most relevant physical regimes, and thus when combined with direct numerical simulations make for excellent use of time and resources.

In recent months, Radu and Susana have also pushed this framework even further to a combined model-predictive control strategy. Here, flow and control information is exchanged on the fly between simplified models and accurate direct numerical simulation in the way that substantially increases the accuracy and efficiency of both methods. This advance allows them to bridge an interdisciplinary gap between rigorous analysis and control theory towards simulation techniques for multi-fluid systems of interest within an integrated methodology of sufficient generalityLink opens in a new window extending to a variety of next-generation technological applications.

Dripping liquid film under the action of an electric field.

Radu Cimpeanu

Susana Gomes