Aqueous foams in microgravity, measuring bubble sizes

TL;DR

This study investigates bubble size evolution in microgravity foams using imaging and diffuse transmission spectroscopy, developing new models for optical measurements and confirming surface bubbles represent bulk foam sizes.

Contribution

The paper introduces a new general expression for diffuse transmitted light intensity applicable to cuboid foam samples and validates surface bubble measurements as representative of bulk foam.

Findings

Surface and bulk bubble sizes agree over time.

New optical model accurately determines average bubble radius.

Surface analysis reflects bulk foam bubble distribution.

Abstract

The paper describes a study of wet foams in microgravity whose bubble size distribution evolves due to diffusive gas exchange. We focus on the comparison between the size of bubbles determined from images of the foam surface and the size of bubbles in the bulk foam, determined from Diffuse Transmission Spectroscopy (DTS). Extracting the bubble size distribution from images of a foam surface is difficult so we have used three different procedures : manual analysis, automatic analysis with a customized Python script and machine learning analysis. Once various pitfalls were identified and taken into account, all the three procedures yield identical results within error bars. DTS only allows the determination of an average bubble radius which is proportional to the photon transport mean free path $\ell^*$. The relation between the measured diffuse transmitted light intensity and {$\ell^*$} previously derived for slab-shaped samples of infinite lateral extent does not apply to the cuboid geometry of the cells used in the microgravity experiment. A new more general expression of the diffuse intensity transmitted with specific optical boundary conditions has been derived and applied to determine the average bubble radius. The temporal evolution of the average bubble radii deduced from DTS and of the same average radii of the bubbles measured at the sample surface are in very good agreement throughout the coarsening. Finally, ground experiments were performed to compare bubble size distributions in a bulk wet foam and at its surface at times so short that diffusive gas exchange is insignificant. They were found to be similar, confirming that bubbles seen at the surface are representative of the bulk foam bubbles.