Moving contact lines and Langevin formalism

Abstract

HypothesisIn previous work [J.-C. Fernández-Toledano, T. D. Blake, J. De Coninck, J. Colloid Interface Sci. 540 (2019) 322–329], **we used molecular dynamics (MD) to show that the thermal oscillations of a contact line formed between a liquid and a solid at equilibrium may be interpreted in terms of an overdamped 1-D Langevin harmonic oscillator. The variance of the contact-line position and the rate of damping of its self-correlation function enabled us to determine the coefficient of contact-line friction ζ and so predict the dynamics of wetting. We now propose that the same approach may be applied to a moving contact line. MethodsWe use the same MD system as before, a liquid bridge formed between two solid plates, but now we move the plates at a steady velocity Uplate in opposite directions to generate advancing and receding contact lines and their associated dynamic contact angles θd. The fluctuations of the contact-line positions and the dynamic contact angles are then recorded and analyzed for a range of plate velocities and solid-liquid interaction. FindingsWe confirm that the fluctuations of a moving contact line may also be interpreted in terms of a 1-D harmonic oscillator and derive a Langevin expression analogous to that obtained for the equilibrium case, but with the harmonic term centered about the mean location of the dynamic contact line xd, rather than its equilibrium position x0, and a fluctuating capillary force arising from the fluctuations of the dynamic contact angle around θd, rather than the equilibrium angle θ0. We also confirm a direct relationship between the variance of the fluctuations over the length of contact line considered Ly, the time decay of the oscillations, and the friction ζ. In addition, we demonstrate a new relationship for our systems between the distance to equilibrium xd-x0 and the out of equilibrium capillary force γLcosθ0-cosθd, where γL is the surface tension of the liquid, and show that neither the variance of the fluctuations nor their time decay depend on Uplate. Our analysis yields values of ζ nearly identical to those obtained for simulations of spreading drops confirming the common nature of the dissipation mechanism at the contact line.