Covariance-Driven Momentum Rectification at Liquid-Vapor Interfaces Near Wetting Transitions

Abstract

Zero-mean forcing can generate directed transport when a medium responds in a spatially structured way and the relevant symmetries are broken. Liquid-vapor interfaces are a useful setting for this problem because surface-tension gradients, wetting dynamics, vapor exchange, capillary and acoustic waves, electro-ionic screening, thermal noise, and boundary compliance can all carry momentum. We develop a conservative continuum model in which the central object is the covariance between a local response field and a zero-mean tangential drive, $\langle Mf\rangle-\langle M\rangle\langle f\rangle$, embedded in an explicit momentum ledger. In a minimal diffuse-interface realization, this covariance gives the phase-selective drift law $U\propto\epsilon_h\Theta\sin\varphi$ for a Marangoni-driven liquid-vapor interface above a structured wall, with exact nulls when the symmetry is restored. Wetting susceptibility then acts as a bounded gain factor: first-order spinodal conditions provide the useful amplification regime, critical wetting saturates because interfacial unbinding removes the short-range drive, and bulk criticality suppresses the channel as the interface disappears. Additional reservoirs - phase change, waves, thermal transport, electro-ionic coupling, compliance, and fluctuations - are treated as compensating channels to be isolated by sign reversals, scaling laws, and budget closure. The result is neither a new microscopic force nor an apparatus-level claim, but a symmetry-constrained accounting scheme for rectified momentum transfer in water-based interfacial systems. Reduced numerical calculations illustrate the phase-selection rules, bounded spinodal gain, momentum-budget closure, transverse chirality, and grid convergence.