Dynamics of Wetting Layer Formation
Daniel Bonn, Emanuel Bertrand, Jacques Meunier, Ralf Blossey
2000
Physical Review Letters
We study the formation and growth of wetting layers in the binary liquid mixture cyclohexanemethanol. By progressively deuterating the methanol we can tune the equilibrium wetting layer thickness. Hysteresis of the transition is observed for large thicknesses and is absent for thinner ones. This can be understood by calculating the activation energy for wetting layer nucleation as a function of the film thickness. We also show that the late-stage growth of the wetting layer after the nucleation
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... process follows a power law in time, in agreement with a diffusion-limited growth mechanism proposed theoretically. PACS numbers: 68.45.Gd, When a liquid droplet is put onto a surface, two situations (distinguishable by the contact angle) may result [1] . If the contact angle is zero, the droplet spreads across the surface, a situation referred to as complete wetting. Second, if the contact angle is between zero and 180 ± , the droplet does not spread, a situation called partial wetting. A wetting transition is a surface phase transition from partial wetting to complete wetting. The wetting transition is generally first order (discontinuous), implying a discontinuity in the first derivative of the surface free energy [1] . Two key observations demonstrate this: the observation of metastable states and of prewetting transitions away from bulk two-phase coexistence [2] . Although the latter has been confirmed for a number of systems, the situation for the metastable states is less clear. In some systems, a clear hysteresis is observed [2], whereas in others no such observation is made [3] . This obviously results from a difference in the dynamics of these wetting phase transitions, i.e., the nucleation and growth of the stable phase. Although detailed theories of wetting dynamics exist [4, 5] , few experiments have been performed. The formation of wetting films after a quench [6] was shown to agree quantitatively with a theory of droplet nucleation [7] . However, since for this system the equilibrium wetting behavior is not known, the dynamics cannot be related to the phase behavior. It is the purpose of the present Letter to study the dynamics of wetting in a system whose equilibrium wetting properties are well known. We show, by studying different binary liquid systems, that there is a simple explanation for the observation or not of hysteresis in experiment, which is due to the presence of gravity. Although in theory the equilibrium wetting layer thickness is infinite, due to the repulsive van der Waals forces, in practice it is large but finite, due to the attractive gravitational potential [8] . Studying systems with varying density differences, we observe a hysteresis for large wetting film thickness (small density difference), but not for small thicknesses. Calcu-lating the nucleation probability for the thick film, it turns out that the nucleation probability decreases rapidly with increasing film thickness so that in some cases long-lived metastable states can indeed be observed, whereas in other cases they cannot. We also show that the growth of the wetting layer towards its final equilibrium state is driven by the long-range van der Waals forces and limited by diffusion. Thus we arrive at a complete characterization of the dynamics of this first-order surface phase transition. We study the demixed binary liquid system of cyclohexane and methanol at the critical composition. Previous studies [2, 9] demonstrated that upon approaching the upper consolute temperature T c from below, a wetting layer of the heavier methanol-rich phase intrudes between the cyclohexane-rich phase and the vapor. Three different kinds of methanol are used, which differ in their degree of deuteration: one is normal methanol ͑CH 3 OH͒, one is partly deuterated ͑CH 3 OD͒, and one is completely deuterated ͑CD 3 OD͒. This specific system is used because for normal methanol, the two liquid phases are almost density matched. By progressive deuteration, we can subsequently reach density differences characteristic of those for other binary liquid systems [3] . The main effect of the deuteration is a change in the density difference. The other parameters, notably the Hamaker constant A, remain virtually unchanged. Explicit calculation, following the method outlined by Israelachvili [10], yields A 8.5 6 0.5 3 10 223 J for the three systems ͑T 25 ± C͒. Ellipsometry [11] is used to study the thickness of the wetting layer. The measured quantity is the ellipticity at the Brewster angle; using the Drude equation [12] , the ellipticity can be related to the integral of the dielectric constant profile in the interfacial region. Considering the intruding wetting layer as a slab, the ellipticity is directly proportional to the thickness of the wetting layer. Here, we are interested only in the formation of the equilibrium wetting layer, starting out from a thin film. We consequently discuss the dynamics of wetting and do 0031-9007͞00͞84(20)͞4661(4)$15.00
doi:10.1103/physrevlett.84.4661
pmid:10990765
fatcat:6l3rvzluobaofg3bnh4tjg5pry