Eur. Phys. J. E (2008) 25: 103-115
https://doi.org/10.1140/epje/i2007-10268-2

Regular Article

Intrusion of fluids into nanogrooves

How geometry determines the shape of the gas-liquid interface

¹ Fakultät für Mathematik und Naturwissenschaften, Technische Universität Berlin, Straße des 17. Juni 135, 10623, Berlin, Germany
² Department of Mathematics, Imperial College, SW7 2BZ, London, UK
³ Departamento de Fısica, Universidad Autónoma Metropolitana-Iztapalapa, Apdo. Postal 55-534, 09340, México D.F., Mexico

^* e-mail: holger.bohlen@fluids.tu-berlin.de
^** e-mail: a.o.parry@ic.ac.uk
^*** e-mail: diaz@xanum.uam.mx
^**** e-mail: martin.schoen@fluids.tu-berlin.de

Received: 18 October 2007
Accepted: 11 January 2008
Published online: 27 February 2008

Abstract

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density ρ(z) along the midline (x = 0 of the nanogroove for various geometries (i.e., depths D and widths L of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk ρ^g,l _x and the interfacial tension γ . The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of ρ(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.