Moving contact lines and Langevin formalism.

We 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 x, rather than its equilibrium position x, and a fluctuating capillary force arising from the fluctuations of the dynamic contact angle around θ, rather than the equilibrium angle θ. We also confirm a direct relationship between the variance of the fluctuations over the length of contact line considered L, 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 x-x and the out of equilibrium capillary force γcosθ-cosθ, where γ is the surface tension of the liquid, and show that neither the variance of the fluctuations nor their time decay depend on U. 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.