Wetting macroscopic theory

For truly nanoscopic capillaries several factors that can lead to deviations from macroscopic theory have been identified. A first step in including these effects in the theory of capillarity has been described in section 11.2.4. It was shown how the capillary pressure can be found, taking into account the presence of a wetting film through the use of Derjaguin s disjoining pressure. 

Another very complicated problem where the approach to equilibrium with time after a quenching experiment is described by an asymptotic law is the owth of wetting layers, in a situation where thermal equilibrium would require the surface to be coated with a macroscopically thick film, but is initially nonwet. For a short-range surface potoitial as discussed in section 3.5, analytical theories predict for a non-conserved density a growth of the thicknm of the layer according to a law f(t) oc In t, and this has in fact been observed by simulations . In the case where the surface potential decays with stance z from the surface as z, the prediction for the thickness l(t) is for the nonconserved case and... 

In the absence of equilibrium, say, over molecular length scales at the interfaces, it is possible to have S > 0, although it is difficult on a macroscopic scale to differentiate between whether 5 = 0 or 5 > 0. This distinction is important since experiment and theory indicate that the larger positive 5 is, the better the spreading over a solid surface is (de Gennes 1985). We discuss the case of complete wetting (0 = 0) here since we shall be concerned with it in Sections 10.3 and 10.5. 

We review a recently developed molecular-based approach for modeling mercury porosimetry. This approach is built on the use of a lattice model of the porous material microstructure and the use of mean-field density fiuictional theory (MF-DFT) calculations and Monte Carlo simulations to calculate the three-dimensional density distribution in the system. The lattice model exhibits a symmetry between the adsorption/desorption of a wetting fluids and intnision/extrusion of a nonwetting fiuid. In consequence, macroscopic approaches used previously to transform mercury porosimetry curves into gas adsorption iso erms are essentially exact in the context of the model. We illustrate the approach with some sample results for intrusion and extrusion in Vycor and controlled pore glass (CPG). 

On the nanoscale the shape of such droplets can deviate significantly from the macroscopic shape of a spherical cap due to the finite range of the intermolecular interactions involved. As described later, one can actually relate the macroscopic equilibrium contact angle, the character of wetting transitions, and the shape of nanodroplets to the intermolecular interactions by using, for example, classical density functional theory (DFT). But the long range of intermolecular interactions also affects the motion of droplets. In particular it can lead to lateral interactions between droplets and structures, which are absent on the macroscopic scale. 

In this case the comparison between experiment and theory is more straightforward, and any deviation from the macroscopic wetting behavior due to microscopic effects can be readily discerned through the analysis of the droplet profile. Among the most studied substrates are freshly cleaved mica and chemically passivated silicon. The surface of freshly cleaved mica is atomically... 

In order to discuss issues raised before about the validity of macroscopic descriptions at nanometer scale, we use some numerical results dedicated to the description of nanomeniscus properties. Using numerical methods (lattice gas model and mean held density functional theories) Jang et al. studied the influence of RH on the pull-off force of a tip on a surface. They reproduced the behavior with a maximum observed with highly hydrophilic rounded tips surfaces (see section 9.3.1.1) and proposed other scenarios for different wetting conditions. 

This consideration shows the rather complicated picture of flow after the meniscus starts to advance macroscopically. This is the reason why the theory of spreading is well developed in the case of complete wetting and is still to be developed in the case of partial wetting. 

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