Modeling of dynamic wetting far from equilibrium

Abstract

In this paper we present simulations of dynamic wetting far from equilibrium based on phase field theory. In direct simulations of recent experiments ͓J. C. Bird, S. Mandre, and H. A. Stone, Phys. Rev. Lett. 100, 234501 ͑2008͔͒, we show that in order to correctly capture the dynamics of rapid wetting, it is crucial to account for nonequilibrium at the contact line, where the gas, liquid, and solid meet. A term in the boundary condition at the solid surface that naturally arises in the phase field theory is interpreted as allowing for the establishment of a local structure in the immediate vicinity of the contact line. A direct qualitative and quantitative match with experimental data of spontaneously wetting liquid droplets is shown.

Universality in dynamic wetting dominated by contact-line friction

“…A non-monotonicity in µ f is observed for pure water for the SiO 2 and silane coating, the same dependency was reported in [14] when comparing with similar experiments [2]. We can at the present time not explain this non-monotonicity for pure water.…”

“…If accounting for the effects of convection of the concentration, that would equal the flux due to gradients of the chemical potential, the Cahn-Hilliard equation is recovered, which along with the Navier Stokes equations forms a theoretical basis for modeling of wetting [14] with a no-slip on the wall.…”

“…To obtain the experimentally observed spreading behavior, an additional dissipation at the contact line was necessary through a non-zero µ f [14]. µ f was determined by obtaining a direct agreement between simulations and experiments, enabling a direct measurement of µ f even in the presence of other contributions such as viscosity and inertia [15].…”

“…By integrating experiments and axi-symmetric simulations based on the Cahn-Hilliard Navier Stokes equations [14,15] we estimate values for the friction factor (µ f ) that appears in the free energy formulation. Theoretically, the friction factor generates a local dissipation at the contact line through its boundary condition.…”

Wall energy relaxation in the Cahn–Hilliard model for moving contact lines

“…Qian et al 15 included such relaxation in their computation of the Couette flow but did not examine its effect. The simulation of Carlson et al 16 indicated that wall relaxation tends to inhibit the motion of the contact line and reduce the speed of drop spreading. But the mechanism for this is unclear.…”