Extended capillary-wave model for the liquid-vapor interface and its width in the limit of vanishing gravity

Victor Romero-Rochín, Carmen Varea and Alberto Robledo

Physica A: Statistical Mechanics and its Applications, 1992, vol. 184, issue 3, 367-392

Abstract: An extended capillary-wave model is derived from density functional theory and the predictions of the usual capillary-wave model are reexamined. The model is expressed in terms of the direct correlation function C(r, r') of the equilibrium fluid. A small wavevector expansion of C(r, r') reduces the extended model to the usual one but it is shown that higher-order terms also play a role in determining interfacial properties in the limit of vanishing gravity. The meaning of the root-mean-square fluctuation W of the distortions of the Gibbs dividing surface and its relation to the actual width Ω of the density profile are specified. For spatial dimensions d < 3 the predictions of the extended and the usual models agree. Explicit calculations for d = 3 show W ∼ In (Lc/a) with Lc the classical capillary length and a a length proportional to the fourth transverse moment of C(r, r'). Adoption of a scaling hypothesis near g → 0, similar to that proposed by Weeks, shows that a ∼ Lc and W does not diverge as g → 0. It is argued that this does not necessarily imply that the width Ω is also finite, although this remains a possibility. Extensions to Week's hypothesis are also examined.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:184:y:1992:i:3:p:367-392

DOI: 10.1016/0378-4371(92)90312-E

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