Reconstruction of tomographic images of dry aqueous foams

Abstract

X-ray tomography offers the possibility to examine the local changes in the structure of a three-dimensional aqueous foam as it flows, allowing a better fundamental understanding of foam rheology and the validation of models. We present an automated algorithm that reconstructs a dry aqueous foam from such images. Our algorithm uses ImageJ to extract from an image the topology of the network of Plateau borders in the foam, and then analyses this network to re-create the films and then the bubbles, and equilibrates the structure in Surface Evolver. We validate our algorithm and demonstrate its precision by applying it to simulated foam structures and analysing the topology and geometry obtained. We then apply our algorithm to a sequence of images from an experiment in which a spherical bead falls under its own weight through a polydisperse dry foam. This allows us to describe the evolution of the foam's liquid content and the bubble volumes with time as well as the distribution of bubble pressure and the forces exerted on a falling sphere.

Using Surface Evolver to measure pressures and energies of real 2D foams submitted to quasi-static deformations

“…But the reconstruction of such structures under SE requires an automated procedure. Davies et al (9) have recently demonstrated a way to build the latter and to obtain an SE equilibrated structure close to the experimental foam structure. The procedure described in the current paper could be applied to 3D structures to obtain a better description of the pressures inside the bubbles by including a feedback control parameter to better adjust the volume of the SE reconstructed bubbles to the experimental ones.…”

“…It is thus well adapted to large collections of images since it is not time or memory consuming: it is thus possible to follow the dynamics of a 2D foam in the quasi-static regime. In addition this method should be transposable to the reconstruction of 3D foams starting from a method like the one described in Davies et al (9).…”

Three-dimensional foam flow resolved by fast X-ray tomographic microscopy

“…Plastic rearrangements -Automated tracking of bubble rearrangements was hindered by the high sensitivity of such procedure to small defects in the reconstruction of the bubble topology. Description of the contact between bubbles requires to rebuild precisely the faces between bubbles, which would require a finer analysis [22]. Nevertheless, we managed to detect manually four individual events, corresponding to the rearrangements of neighboring bubbles.…”

“…Such experimental results could be achieved thanks to the recent advances of both high resolution and fast X-ray tomography and quantitative analysis tools. Perspectives include further refinements of the reconstruction methods [15,22], to fully automatize the detection of rearrangements, to increase statistics and to study various geometries. Imaging the 3D flow at the bubble scale may shed new light on pending issues on shear localization [9] and nonlocal rheology [29].…”

Using positron emission tomography (PET) to determine liquid content in overflowing foam

“…Recently, X-ray tomography and radioscopy have been used to measure significant changes in liquid content from changes in density with time, whilst additionally revealing the internal structure of foams on the micro-scale. Davies et al (2013) used X-ray micro-tomography to image a small sample of foam at very high spatial resolution, and Solórzano et al (2013) used X-ray radioscopy in two modes to measure the liquid content and bubble size of beer foams. So far, these X-ray techniques rely on small active areas and, as such, have only been applied to small experimental systems.…”