Abstract
Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width is considered. Under the condition that the wall is only partially wet (or dry) while the stripe tends to be wet completely, a liquid drop is formed above the stripe. The maximum height of the drop depends on the stripe width and the chemical potential departure from saturation where it adopts the value . Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that is approached linearly with with a slope which scales as over the region satisfying , where is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve to which the adsorption isotherms corresponding to different values of all collapse when appropriately rescaled. Although the series expansion based on the interfacial Hamiltonian model can be formed by considering higher order terms, a more appropriate approximation in the form of a rational function based on scaling arguments is proposed. The approximation is based on exact asymptotic results, namely, that for and that obeys the correct behavior in line with the results of the interfacial Hamiltonian model. All the predictions are verified by the comparison with a microscopic density functional theory (DFT) and, in particular, the rational function approximation—even in its simplest form—is shown to be in a very reasonable agreement with DFT for a broad range of both and .
- Received 22 September 2020
- Accepted 10 November 2020
DOI:https://doi.org/10.1103/PhysRevE.102.052802
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