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 \(\phi\) 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.