Height of a liquid drop on a wetting stripe
| Autor: | Alexandr Malijevský |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Condensed Matter - Materials Science Condensed Matter - Mesoscale and Nanoscale Physics Statistical Mechanics (cond-mat.stat-mech) Condensed matter physics Universal curve Liquid drop Materials Science (cond-mat.mtrl-sci) FOS: Physical sciences Rational function symbols.namesake Mesoscale and Nanoscale Physics (cond-mat.mes-hall) symbols Density functional theory Wetting van der Waals force Series expansion Scaling Condensed Matter - Statistical Mechanics |
| Zdroj: | Physical Review E. 102 |
| ISSN: | 2470-0053 2470-0045 |
| Popis: | Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of width $L$ 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 ${\ensuremath{\ell}}_{m}(\ensuremath{\delta}\ensuremath{\mu})$ of the drop depends on the stripe width $L$ and the chemical potential departure from saturation $\ensuremath{\delta}\ensuremath{\mu}$ where it adopts the value ${\ensuremath{\ell}}_{0}={\ensuremath{\ell}}_{m}(0)$. Assuming a long-range potential of van der Waals type exerted by the stripe, the interfacial Hamiltonian model is used to show that ${\ensuremath{\ell}}_{0}$ is approached linearly with $\ensuremath{\delta}\ensuremath{\mu}$ with a slope which scales as ${L}^{2}$ over the region satisfying $L\ensuremath{\lesssim}{\ensuremath{\xi}}_{\ensuremath{\parallel}}$, where ${\ensuremath{\xi}}_{\ensuremath{\parallel}}$ is the parallel correlation function pertinent to the stripe. This suggests that near the saturation there exists a universal curve ${\ensuremath{\ell}}_{m}(\ensuremath{\delta}\ensuremath{\mu})$ to which the adsorption isotherms corresponding to different values of $L$ 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 ${\ensuremath{\ell}}_{m}\ensuremath{\sim}\ensuremath{\delta}{\ensuremath{\mu}}^{\ensuremath{-}1/3}$ for $L\ensuremath{\rightarrow}\ensuremath{\infty}$ and that ${\ensuremath{\ell}}_{m}$ obeys the correct $\ensuremath{\delta}\ensuremath{\mu}\ensuremath{\rightarrow}0$ 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 $\ensuremath{\delta}\ensuremath{\mu}$ and $L$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|