The surface tells it all: Relationship between volume and surface fraction of liquid dispersions

TL;DR

This paper establishes a relationship between the volume fraction of the continuous phase in liquid dispersions and the wetted surface fraction at a wall, providing a practical optical method for estimating dispersion properties.

Contribution

It introduces a novel method linking surface wetted fraction to volume fraction in dispersions, combining experimental and theoretical approaches.

Findings

Surface wetted fraction correlates with volume fraction in foams.

Optical measurement of surface fraction enables estimation of dispersion properties.

The relationship aids understanding of rheology and aging in liquid dispersions.

Abstract

The properties of liquid dispersions, such as foams or emulsions, depend strongly on the volume fraction $\phi$ of the continuous phase. Concentrating on the example of foams, we show experimentally and theoretically that $\phi$ may be related to the fraction $\phi_s$ of the surface at a wall which is wetted by the continuous phase - given an expression for the interfacial energy or osmotic pressure of the bulk system. Since the surface fraction $\phi_s$ can be readly determined from optical measurement and since there are good general approximations available for interfacial energy and osmotic pressure we thus arrive at an advantageous method of estimating $\phi$. The same relationship between $\phi$ and $\phi_s$ is also expected to provide a good approximation of the fraction of the bubble or drop surface which is wetted by the continuous phase. This is a parameter of great importance for the rheology and ageing of liquid dispersions.