Confocal imaging and second‐order stereological analysis of a liquid foam

Abstract

Foam structures are found in diverse fields of study; the structure of fire‐fighting foam, upholstery foams and even the head on a pint of beer all share detailed similarities in their microstructure and dynamics. Despite impressive developments in the theory of two‐dimensional foams the challenge in future will be to analyse and model the dynamics of three‐dimensional foams. However, the myriad of gas/liquid interfaces in an aqueous foam make direct imaging of their structure difficult. In this study we circumvent this problem by using fluorescence confocal microscopy to acquire three‐dimensional images of the structure of a coarsening aqueous foam.A stable aqueous foam was created by mixing commercial shaving foam with ethanol and a small amount of fluorescein solution. The foam was imaged in fluorescence mode such that the liquid fraction of the foam, containing the fluorescent dye, could be seen in optical sections. These images could be acquired in three‐dimensional stacks of optical sections up to a depth of about 200 μm. Single images were also acquired as a time series.The time series of single optical section images clearly show the dynamics of the foam. Early images show a structure made mainly of spherical bubbles; later images show the polyhedral structure of the foam which coarsens as a function of time. The polyhedral nature of the foams is shown particularly clearly in stereo pair images of the three‐dimensional image sets. The three‐dimensional images of the foams were also analysed using second‐order stereology (statistical summaries of spatial distribution). The x, y and z coordinates of the foam vertices were extracted from the images and used to compute the nearest neighbour (G‐function) and reduced second moment (K‐function) statistics. These statistics allow quantification of the range of length scales found in the foams. These results form part of an ongoing study of the coarsening of aqueous foams.