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

The properties of liquid dispersions, such as foams or emulsions, depend strongly on the volume fraction $\varphi$ of the continuous phase. Concentrating on the example of foams, we show experimentally and theoretically that $\varphi$ may be related to the fraction ${\varphi }_s$ 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 ${\varphi }_s$ 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 $\varphi$. The same relationship between $\varphi$ and ${\varphi }_s$ 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.