Asymptotic properties of bridging transitions in sinusoidally-shaped slits

TL;DR

This paper investigates the asymptotic behavior of bridging transitions in sinusoidally-shaped slits, revealing how wall roughness and parameters influence transition types and scaling laws, verified through density functional theory.

Contribution

It introduces a detailed analysis of bridging transitions in sinusoidal walls, highlighting the effects of wall roughness reduction methods and establishing new scaling laws verified numerically.

Findings

Bridging film thickness diverges as $k^{-2/3}$ when $k o 0$.

Transition location approaches capillary condensation as $k^{2/3}$.

Existence of a minimal amplitude $A_{min}(k,L)$ below which bridging does not occur.

Abstract

We study bridging transitions that emerge between two sinusoidally-shaped walls of amplitude $A$, wavenumber $k$, and mean separation $L$. The focus is on weakly corrugated walls to examine the properties of bridging transitions in the limit when the walls become flat. The reduction of walls roughness can be achieved in two ways which we show differ qualitatively: a) By decreasing $k$, (i.e., by increasing the system wavelength), which induces a continuous phenomenon associated with the growth of bridging films concentrated near the system necks, the thickness of with the thickness of these films diverging as $\sim k^{-2/3}$ in the limit of $k\to0$. Simultaneously, the location of the transition approaches that of capillary condensation in an infinite planar slit of an appropriate width as $\sim k^{2/3}$; b) in contrast, the limit of vanishing walls roughness by reducing $A$ cannot be considered in this context, as there exists a minimal value $A_{\rm min}(k,L)$ of the amplitude below which bridging transition does not occur. On the other hand, for amplitudes $A>A_{\rm min}(k,L)$, the bridging transition always precedes global condensation in the system. These predictions, including the scaling property $A_{\rm min}\propto kL^2$, are verified numerically using density functional theory.