Thin-film model of droplet durotaxis

Abstract

The control of liquid droplets on solid surfaces is important in many scientific and technological applications, including microfabrication, microfluidics and heat transfer. It has been known for decades that droplets sitting on a solid surface can be moved using thermal, chemical or electrical gradients. Recent experiments have shown that gradients of substrate deformability also produce spontaneous droplet motion. This motion mechanism, which is called durotaxis, remains poorly understood. This paper proposes a model for droplet durotaxis based on a thin-film description of the fluid dynamics equation. The substrate is modeled as a Kirchhoff plate with non-constant flexural rigidity. We use high-fidelity simulations to show that the model naturally predicts droplet durotaxis without any ad hoc assumption. The model predictions for the dependence of droplet velocity on droplet size are consistent with experiments. The simplicity of the model suggests that durotaxis may be a pervasive and fundamental process at small scales and opens new possibilities to study the interaction of droplets with compliant solid surfaces.