title: Young's Equation for a Two-Liquid System on the Nanometer Scale.
abstract: We use large-scale molecular dynamics simulations to study the Lennard-Jones forces acting at the various interfaces of a liquid bridge (liquid 1) between two realistic solid plates on the scale of few nanometers when the two free surfaces are in contact with a second immiscible liquid (liquid 2) with an interfacial tension of γ12. Each plate comprises a regular square planar lattice of atoms arranged in three atomic layers. To maintain rigidity while allowing momentum exchange with the liquid, solid atoms are allowed to vibrate thermally around their initial positions by a strong harmonic potential. By varying the solid-liquid coupling, we investigate a range of nonzero contact angles between the liquid-liquid interface and the solid. We first compute the forces when the plates are stationary (equilibrium case), from the perspectives of both the liquid and the solid. Our results confirm that the normal and tangential components of the computed interfacial forces at each contact line are consistent with Young's equation on this small scale. In particular, we show that the tangential force exerted by the liquid-liquid interface on the plates is given by the difference in the individual works of adhesion of the two liquids and equal to γ12cos θ1,20, where θ1,20is the equilibrium contact angle measured through liquid 1. This result, which differs from that expected for a single liquid, is relevant to the interactions and behavior of two liquid-solid systems in nanotechnology. We then study the forces when the plates are translated at equal speeds in opposite directions over a range of steady velocities (dynamic case) and repeat the measurements of the force exerted by the liquid-liquid interface on the solid. We find that the normal and tangential components of this force are still correctly predicted by the normal and tangential components of the interfacial tension, provided only that the equilibrium contact angle is replaced by its dynamic analogue θ1,2D. Usually assumed without proof, this result is significant for our proper understanding of dynamic wetting at all scales.
authors.affiliation: Laboratory of Surface and Interfacial Physics (LPSI), University of Mons , 7000 Mons, Belgium.
authors.forename: J-C
authors.identifier: 0000-0002-5482-3104
authors.initials: JC
authors.lastname: Fernandez-Toledano
authors.affiliation: Laboratory of Surface and Interfacial Physics (LPSI), University of Mons , 7000 Mons, Belgium.
authors.forename: T D
authors.initials: TD
authors.lastname: Blake
authors.affiliation: Laboratory of Surface and Interfacial Physics (LPSI), University of Mons , 7000 Mons, Belgium.
authors.forename: J
authors.initials: J
authors.lastname: De Coninck