Thermally Activated Wetting Dynamics in the Presence of Surface Roughness Kristina Davitt,* ,† Michael S. Pettersen, ‡ and Etienne Rolley † † Laboratoire de Physique Statistique, Ecole Normale Supé rieure, UPMC Univ Paris 06, Universite ́ Paris Diderot, CNRS, 24 rue Lhomond, 75005 Paris, France ‡ Department of Physics, Washington and Jefferson College, Washington, Pennsylvania 15301, United States ABSTRACT: From simple models of thermally activated contact line dynamics far below the depinning transition, one expects the velocity to depend exponentially on the applied force and the activation area to be the size of the defects on the surface. We study contact line motion on evaporated gold films and find that the dynamics are activated, but the activation area is not straightforwardly linked to the surface roughness. Surprisingly, the activation area can be significantly smaller than any features on the surface. Furthermore, it depends strongly on the liquid. We show that this indicates that the line is close to the depinning threshold at experimentally accessible velocities. A model based on independent defects is developed and used to show deviations from the purely exponential law. The dynamics are written entirely in terms of properties of the surface and partially wetting liquid. In addition, we are able to show that the region of validity of models of thermal activation on mesoscopically rough surfaces typically corresponds to velocities of less than 1 mm/s. ■ INTRODUCTION How a liquid spreads on a solid is strongly influenced by the disorder on the surface. This is at once a practical issue − as many ordinary surfaces are either chemically or topographically heterogeneous, if not on the optical scale then at the nanometric scale − and a general one 1 since it is an example of an elastic interface in a disordered medium, much like magnetic domain walls 2 or crack front propagation. 3 In accordance with Young’s law, γ cos θ eq = γ SV − γ SL , the equilibrium contact angle θ eq for a liquid on a solid surface is determined by the set of interfacial tensions between the liquid, vapor, and solid (γ = γ LV , γ SV , γ SL ). However, one finds that θ eq is not experimentally accessible, but that the measured angle depends on the history of the contact line. Consider a drop placed on a solid surface: the contact angle slowly decreases as it relaxes toward equilibrium, and the velocity of the contact line gets progressively slower. In practice, equilibrium is never strictly achieved and the velocity never reaches zero, even if it is well below experimental resolution. Instead, it has become standard to report angles for very slowly advancing (θ A ) or receding (θ R ) contact lines, which allows us to define a hysteresis H = γ(cos θ R − cos θ A ) > 0. It has been understood for some time that this hysteresis is attributed to pinning of the contact line on disorder present on the solid surface. 4,5 On the other hand, the dynamics of this pinning and depinning process, or how the velocity of the contact line depends on the unbalanced Young force at low velocity, is still very often neglected. There are a number of well-developed models of wetting dynamics, including the molecular kinetic theory (MKT), which considers dissipation at the contact line due to molecular-scale activated processes, 6 and hydrodynamic mod- els, which account for bulk viscous dissipation 5 that becomes important for larger capillary numbers, Ca = ηυ/γ, where η is the liquid viscosity and υ the velocity. It is important to note that much like the Young equation, these models were developed with the assumption of perfect surfaces and one can ask under what conditions they can be used in the presence of disorder. In this article, we study contact line motion at very low capillary numbers, Ca = 10 −5 to 5 × 10 −11 , on surfaces with mesoscale roughness (10−100 nm) and therefore expect a priori to find that activated processes dominate. The relationship between nanoroughness and hysteresis 7,8 has been studied experimentally, and the hysteresis has been found to depend on the size and density of defects. Also, measurements of the dynamics on molecular layers 9,10 have been made; however, to our knowledge no systematic study of activated dynamics has been done on surfaces of controlled topographical disorder in order to directly link measurable surface and liquid properties to the dynamics. In a previous study of liquid hydrogen on evaporated cesium surfaces, 11 it was found that the activation area was on the order of the size of the grains of cesium, but it is difficult to modify and measure the disorder in cryogenic systems and a limited range of velocities was explored. Here, we have developed a room- temperature analog to this system where (i) the surface Received: February 25, 2013 Revised: April 25, 2013 Published: May 24, 2013 Article pubs.acs.org/Langmuir © 2013 American Chemical Society 6884 dx.doi.org/10.1021/la400649h | Langmuir 2013, 29, 6884−6894