Continuous condensation in nanogrooves

Abstract

We consider condensation in a capillary groove of width $L$ and depth $D$, formed by walls that are completely wet (contact angle $\theta =0$), which is in a contact with a gas reservoir of the chemical potential $\mu$. On a mesoscopic level, the condensation process can be described in terms of the midpoint height $\ell$ of a meniscus formed at the liquid-gas interface. For macroscopically deep grooves ($D\to \infty$), and in the presence of long-range (dispersion) forces, the condensation corresponds to a second order phase transition, such that $\ell \sim ({\mu }_{cc}-\mu {)}^{-1/4}$ as $\mu \to {\mu }_{cc}^{-}$ where ${\mu }_{cc}$ is the chemical potential pertinent to capillary condensation in a slit pore of width $L$. For finite values of $D$, the transition becomes rounded and the groove becomes filled with liquid at a chemical potential higher than ${\mu }_{cc}$ with a difference of the order of $D^{-3}$. For sufficiently deep grooves, the meniscus growth initially follows the power-law $\ell \sim ({\mu }_{cc}-\mu {)}^{-1/4}$ but this behaviour eventually crosses over to $\ell \sim D-(\mu -{\mu }_{cc}{)}^{-1/3}$ above ${\mu }_{cc}$, with a gap between the two regimes shown to be $\bar{\delta }\mu \sim D^{-3}$. Right at $\mu ={\mu }_{cc}$, when the groove is only partially filled with liquid, the height of the meniscus scales as ${\ell }^{\ast }\sim (D^{3}L{)}^{1/4}$. Moreover, the chemical potential (or pressure) at which the groove is half-filled with liquid exhibits a non-monotonic dependence on $D$ with a maximum at $D\approx 3L/2$ and coincides with ${\mu }_{cc}$ when $L\approx D$. Finally, we show that condensation in finite grooves can be mapped on the condensation in capillary slits formed by two asymmetric (competing) walls a distance $D$ apart with potential strengths depending on $L$.

References in corpus (6)

• Complete Wetting of Pits and Grooves
• Does adsorption in a single nanogroove exhibit hysteresis?
• Modified Kelvin equations for capillary condensation in narrow and wide grooves
• Capillary Contact Angle in a Completely Wet Groove
• Condensation and evaporation transitions in deep capillary grooves
• Phase transitions of fluids in heterogeneous pores

Cited by in corpus (2)

• Phase behaviour of fluids in undulated nanopores
• Filling, depinning, unbinding: Three adsorption regimes for nanocorrugated substrates