Liquid-Gas Asymmetry and the Wavevector-Dependent Surface Tension

Abstract

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension ${\sigma }_{\text{eff}}(q)$, have encountered difficulties. There is no consensus as to even the shape of ${\sigma }_{\text{eff}}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterised by a microscopic $q$-dependent length $\zeta (q)$ not identified previously. The necessity of including the $q$ dependence of $\zeta (q)$ is illustrated explicitly in our model and has wider implications, i.e. in typical experimental and simulation studies, an indeterminacy in $\zeta (q)$ will always be present, reminiscent of the cut-off used in capillary-wave theory. This leads inevitably to a large uncertainty in the $q$ dependence of ${\sigma }_{\text{eff}}(q)$.

5 pages,1 figure + Supplementary Material (3 pages, 1 figure)

References in corpus (4)

• Description of the fluctuating colloid-polymer interface
• On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
• Enhanced wavelength-dependent surface tension of liquid-vapour interfaces
• Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface