From bipedal to chaotic motion of chemically fueled partially wetting liquid drops

We employ a thermodynamically consistent out-of-equilibrium continuum model to study the motion patterns of partially wetting liquid drops covered by autocatalytically reacting surfactants. When ambient chemostats feed a chemomechanical feedback loop involving a nonlinear reaction network, surface stresses caused by the Marangoni effect and the ensuing hydrodynamic motion, drops show a variety of increasingly complex biomimetic motility modes including shuttling, bipedal, rotational, intermittently chaotic and chaotic motion. We determine the corresponding nonequilibrium phase diagram and show that the complexity of the motion arises from competing length scales.

💡 Research Summary

In this work the authors develop a thermodynamically consistent out‑of‑equilibrium continuum model to investigate the rich motility of partially wetting liquid drops that are covered by two species of insoluble surfactants undergoing an autocatalytic reaction. The drops sit on a flat solid substrate and exchange surfactant material with an ambient bath that acts as a chemostat, continuously supplying chemical fuel and removing waste. A difference in the external chemical potentials (μ_ex₁ ≠ μ_ex₂) drives the system away from equilibrium and creates a chemomechanical feedback loop.

The state variables are the height profile h(x,t) of the drop and the surface densities Γ₁(x,t) and Γ₂(x,t) of the two surfactants. The free‑energy functional consists of a wetting term f(h) (including a Hamaker constant to enforce partial wetting), an entropic term g(Γ₁,Γ₂) for the surfactants, and a capillary term proportional to |∇h|². The surface tension depends linearly on the total surfactant density, γ = γ₀ – k_BT(Γ₁+Γ₂).

Dynamics obey the gradient‑flow‑type equation ∂ₜψ = ∇·