Domain growth dynamics and local viscosity in stratifying foam films

We present a quantitative theory and experiments for the expansion dynamics of domains in stratifying foam films. Foam films containing micelles, colloidal particles or polymer-surfactant complexes often form layered structures and thin in a stepwise fashion: circular domains of lower thickness are formed and expand following a $R\left(t\right)\propto t^{1∕2}$ law. In the present paper the film is modeled by an incompressible three-dimensional fluid with incompressible surfaces. The film tension difference between the film and domains results in the formation of a rim at the domain boundary and a gradient in film thickness and pressure in the surrounding film. The material transport due to this gradient lets the domains grow. We present experiments utilizing the thin balance method to qualitatively confirm the thinning mechanism and to determine material parameters including local film viscosity of a film composed of $4400\mathrm{ppm}$ acrylamide/acrylamidomethylpropanesulfonate-copolymer and $0.06\mathrm{mmol}∕\mathrm{l}$ dodecyltrimethylammonium bromide solution. We found a film viscosity of about 60 times the bulk viscosity, consistent with previous measurement in the same system but using another method.