Anomalous liquid imbibition at the nanoscale: the critical role of interfacial deformations

Abstract

We observed that imbibition of various Rhodamine B-doped wetting liquids in an array of different-sized, horizontal, two-dimensional silica nanochannels terminated within the channels as a function of hydraulic diameter and liquid type. This front termination is not predicted by the classic Washburn equation for capillary flow, which establishes diffusive dynamics in horizontal channels. Various explanations for the anomalous static imbibition measurements were negated; hydrodynamics, thermodynamics, surface chemistry and mechanics were all taken into consideration for this analysis. The atypical imbibition data are explained by deformed menisci and decreased effective channel diameters. These occurrences are due to the enhanced influence of the following phenomena at the nanoscale: surface forces at fluid-solid boundaries, the presence of quasi-crystalline thin films or boundary regions, and potential solid surface or boundary layer deformation due to meniscus-induced negative pressures (suction). We introduce a phenomenological model which demonstrates how van der Waals forces, common to all interfaces, lead to local menisci deformation and an average reduction in capillary pressure. An expression for the approximate capillary pressure of a symmetric nanoscale meniscus in a cylindrical pore space is derived; its difference from the macroscopic capillary pressure can be expressed by an effective contact angle. Precursor films, adsorbed films and elastocapillary deformation decrease effective diameter, exacerbating meniscus deformation and increases in effective viscosity; we also describe local models and effective values for these phenomena. The findings can be scaled to imbibition and two-phase flow in nanoporous media.