https://doi.org/10.1140/epjs/s11734-026-02296-w
Regular Article
Gradient dynamics model for chemically driven running drops
1
Institute of Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149, Münster, Germany
2
Center for Data Science and Complexity (CDSC), University of Münster, Corrensstr. 2, 48149, Münster, Germany
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
30
January
2026
Accepted:
22
March
2026
Published online:
6
April
2026
Abstract
We present a thermodynamically consistent model for chemically driven running drops on a solid substrate with reversible substrate adsorption of a wettability-changing chemical species. We consider drops confined to a vertical gap, thereby allowing us to first obtain a gradient dynamics description of the closed system, corresponding to a set of coupled dynamical equations for the drop profile and the chemical concentration profiles of species on the substrate and in both fluids (drop, ambient medium). Chemostatting the species in the drop and the ambient medium, we then derive a reduced model for the dynamics of the drop and the adsorbate on the substrate. When the externally imposed chemical potentials are distinct, the system is driven away from thermodynamic equilibrium, allowing for sustained drop self-propulsion across the substrate due to a wettability contrast maintained by chemical reactions. We numerically study the resulting running drops and show how they emerge from drift-pitchfork bifurcations.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Justus Niehoff and Florian Voss contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
