Spontaneous Ratchet Currents and Transition Dynamics in Active Wetting

TL;DR

This work analyzes active wetting of self-propelled particles on repulsive barriers using an exact noiseless hydrodynamic limit of an active lattice gas in a slit-like geometry, showing robust fully- and partially-wet states and a critical wetting transition. It reveals a spontaneous symmetry-breaking ratchet current in the partially-wet state, driven by activity rather than geometric asymmetry, which alters steady states and introduces a faster, non-equilibrium dynamical pathway between wetting states. To understand this mechanism, the authors develop a minimal model—a scalar field with a double-well free energy and a localized pump—that reproduces the three-stage full-to-partial transition and yields a finite instability threshold $\eta^*$ for barrier-induced transitions, with $\eta^* = \dfrac{\sqrt{2 \alpha \kappa}}{\coth\left(L \sqrt{\frac{\alpha}{8 \kappa}}\right) - \dfrac{1}{L}\sqrt{\frac{8 \kappa}{\alpha}}}$, tending to $\sqrt{2 \alpha \kappa}$ as $L \to \infty$. The study shows that the partially-wet state supports a steady ratchet current $J^{(\rho)}_{ss}$ that scales as $J^{(\rho)}_{ss} \sim \ell_s^{-1}$ for large system size, and that bulk densities depart from their binodal values due to this nonequilibrium drive, highlighting intrinsic nonequilibrium effects in active wetting. Overall, the work connects equilibrium-like surface phase transitions with genuine nonequilibrium phenomena, suggesting experimental routes using, e.g., light-activated colloids in quasi-1D channels to test active wetting predictions.

Abstract

Self-propelled particles accumulate on repulsive barriers in so-called active wetting, but the relationship between this process and equilibrium wetting remains unclear. Using an exact (noiseless) hydrodynamic framework for an active lattice gas, we show, using a slit geometry with periodic boundary conditions, that active matter exhibits both fully- and partially-wet states, with a critical wetting transition between them. Furthermore, we demonstrate the existence of a spontaneous-symmetry-breaking ratchet current in the partially wet state, leading to departure of the bulk densities from their binodal values and the emergence of a novel dynamical pathway for the full-to-partial wetting transition. We elucidate this modified dynamical pathway using a minimal model. The results, while establishing a direct connection between active and equilibrium wetting, also identify the nonequilibrium consequences of activity.

Figures (4)

• Figure 1: (a.1) Illustration of the system geometry. (a.2) Surface phase diagram; individual points are labelled according to their extrapolated steady-state. (b.1-2) Example full- and partial-wetting states; orientation-dependent density $f(x, \theta, t)$ is shown in colour; arrows show current (arbitrary scale); integrated spatial density $\rho(x, t)$ is shown with overlaid line. (c) Critical wetting phenomena. (c.1) Divergence of the thin film width. (c.2) Pitchfork bifurcation in the asymmetry, scanning $\mathcal{A}$ as a function of $\epsilon$ up (orange) and down (blue). (c.3) Linear stability of a fully-wet initial condition with weak noise; measured at early times, when asymmetry growth is approximately linear. See companion_paper_placeholder for further details of numerics.
• Figure 2: Illustration of steady-state current in the partially-wet state. (a) Steady-state current as a function of system size, tending to $\sim1/\ell_s$. (b) Steady-state current vanishes continuously as $\epsilon \to \epsilon^*$ (same parameters as Figure \ref{['fig:wetting_states']}(c.2)).
• Figure 3: (a.1) Full-to-partial transition pathway at $\text{Pe}=15$. (a.2) $\mathcal{A}(t)$ for this process. (b.1, b.2) Pathway and asymmetry for partial-to-full transition at $\text{Pe}=8$.
• Figure 4: (a) Density profile over time for a full-to-partial transition in the minimal model ($\alpha = \kappa = 1, \eta = 2$). (b) Asymmetry over time. Comparing with Fig \ref{['fig:dynamical_pathways']}(a) one sees that the minimal model captures the three-stage transition found in the full dynamics.