A new experimental method is presented using fluorescein dye to determine the spatial and temporal variations of the liquid volume fraction in aqueous foams This method is used for quantitative studies of liquid redistribution (drainage) in three types of experiments: forced, free, and pulsed drainage Characteristic quantities, such as the drainage velocity, show power-law dependences on experimental parameters that are inconsistent with traditional foam drainage models based on Poiseuille-type flow in the liquid-carrying channels (Plateau borders) of the foam To obtain a theoretical description, the foam drainage equation is generalized using an energy argument which accounts for viscous dissipation in both the channels and the nodes (or vertices, which are the junctions of four channels) of the liquid network Good agreement with results for all three types of drainage experiments is found when using this new model in the limit where the dissipation is dominated by the nodes

https://www.princeton.edu/%7Estonelab/Publications/pdfs/From%20Howard/Langmuir/KoehlerLangmuir00.pdf

A Generalized View of Foam Drainage: Experiment and Theory

This review covers recent advances in the study of foam drainage and coarsening, focusing especially on the effective role of the foam chemical components on those aging processes. The determination of the relevant parameters controlling foam drainage and coarsening today remains a major issue: are the physical parameters (like bubble size and liquid fraction) sufficient to define a foam and to predict its evolution, or do the chemical components also matter? And if these foam components are important, one has to determine by which mechanisms, and which microscopic parameters involved in these mechanisms are eventually crucial. I report here recent experimental results, shedding light on these issues. It allows us to summarize how the surfactant, the liquid bulk properties, and the gas modify or not the drainage and coarsening features. The coupling between drainage and coarsening is also discussed, as well as the role of the experimental conditions (sample height, shape or foam uniformity).

https://perso.univ-rennes1.fr/arnaud.saint-jalmes/review_saintjalmes_drainage_coarsening_final.pdf

Physical chemistry in foam drainage and coarsening

The drainage of liquid in a foam may be described in terms of a nonlinear partial differential equation for the foam density as a function of time and vertical position. We review the history and recent development of this theory, analysing various exact and approximate solutions and relating them to each other.

https://iopscience.iop.org/article/10.1088/0953-8984/8/21/002/pdf

The foam drainage equation

The structure of basaltic scoria and reticulite and inferences for vesiculation, foam formation, and fragmentation in lava fountains

Decay of standing foams: drainage, coalescence and collapse

A theoretical model for interstitial liquid flow in a stationary or moving foam was devised by relating the physical structure of the foam to the physical properties of the surfactant and the foam movement. This was accomplished through a differential momentum balance within a typical capillary (Plateau border) of noncircular cross section with finite surface viscosity at its boundaries. Velocity profiles were then calculated and integrated numerically for the randomly oriented capillaries so as to obtain the overall liquid flow through the foam in terms of the pertinent variables. Results are presented in a form suitable for estimating concentrations and flow rates of product and waste streams in foam fractionation.

A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation

Experimental results obtained over a wide range of variables from three different foam fractionation columns support the theory developed in Part I.

Ralph A. Leonard

Papers

A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation

A study of interstitial liquid flow in foam. Part II. Experimental verification and observations