Gradient dynamics approach to reactive thin-film hydrodynamics

• Published in: Journal of engineering mathematics Vol. 149; no. 1
• Main Authors: Voss, Florian, Thiele, Uwe
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.12.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Chemical reactions; Computational Mathematics and Numerical Analysis; Hydrodynamics; Kinetic equations; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Surfactants; Theoretical and Applied Mechanics; Thin films; Wettability; Wetting; Reactive surfactants; Self-propelled drops; Chemo-mechanical coupling; Reactive thin-film hydrodynamics; Gradient dynamics; Reactive wetting
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-024-10402-x

Wetting and dewetting dynamics of simple and complex liquids is described by kinetic equations in gradient dynamics form that incorporates the various coupled dissipative processes in a fully thermodynamically consistent manner. After briefly reviewing this, we also review how chemical reactions can be captured by a related gradient dynamics description, assuming detailed balanced mass action type kinetics. Then, we bring both aspects together and discuss mesoscopic reactive thin-film hydrodynamics illustrated by two examples, namely, models for reactive wetting and reactive surfactants. These models can describe the approach to equilibrium but may also be employed to study out-of-equilibrium chemo-mechanical dynamics. In the latter case, one breaks the gradient dynamics form by chemostatting to obtain active systems. In this way, for reactive wetting we recover running drops that are driven by chemically sustained wettability gradients and for drops covered by autocatalytic reactive surfactants we find complex forms of self-propulsion and self-excited oscillations.