Hole theory as a prediction tool for Brownian diffusive motion in binary mixtures of liquids

Abstract

The hole theory of liquids has been around for a long time since its development. This theory assumes that a liquid can be seen as a continuum permeated by holes and was developed with the aim of explaining thermal and viscous properties in liquids at equilibrium. It has often been used as a predictive tool for viscosity of liquids, including molten metals, ionic and molecular liquids. However, a direct link to actual transport properties in liquids, i.e., molecular diffusion, has never been fully shown nor validated. This work explores the application of hole theory as a simple tool to understand and predict molecular diffusion at equilibrium in liquids. In particular, a wide range of binary liquid mixtures, ranging from ideal to highly non-ideal, has been assessed by calculating the average hole diffusivity as a function of composition and comparing these values to experimental values of molecular diffusivity at equilibrium. The results show that the average motion of the holes describes very well the average motion of the diffusing species in the mixture and this is ascribed to an inter-diffusion process between the molecular species and the holes. The findings reported here are of importance as they establish a direct link between hole theory and transport properties and validate the use of the theory as an effective and novel way of estimating molecular diffusivity in liquids, which may be challenging to measure or often unavailable, by knowing surface tension and viscosity data, which are widely available in the literature or easier to measure.