Wetting on a spherical wall: Influence of liquidgas interfacial properties
Abstract
We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluidfluid and fluidwall longrange forces. We first reexamine the wetting properties of the model in the zerocurvature limit, i.e., for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharpkink approximation (SKA). We obtain very good agreement with a meanfield density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the socalled softinterface approximation (SIA) originally formulated by Napiórkowski and Dietrich [Phys. Rev. BPRBMDO1098012110.1103/PhysRevB.34.646934, 6469 (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, it turns out that the agreement between SKA and our DFT is only qualitative. We then show that the quantitative discrepancy between the two is due to the overestimation of the liquidgas surface tension within SKA. On the other hand, by relaxing the assumption of a sharp interface, with, e.g., a simple “smoothing” of the density profile there, markedly improves the predictive capability of the theory, making it quantitative and showing that the liquidgas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected meanfield critical exponent of the liquidgas surface tension.
 Publication:

Physical Review E
 Pub Date:
 August 2011
 DOI:
 10.1103/PhysRevE.84.021603
 arXiv:
 arXiv:1103.6125
 Bibcode:
 2011PhRvE..84b1603N
 Keywords:

 68.08.Bc;
 05.20.Jj;
 71.15.Mb;
 05.70.Np;
 Wetting;
 Statistical mechanics of classical fluids;
 Density functional theory local density approximation gradient and other corrections;
 Interface and surface thermodynamics;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 Phys. Rev. E 84, 021603 (2011)