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Soft Matter and Biological Physics

Eur. Phys. J. E 7, 35-44 (2002)
DOI: 10.1140/epje/i200101092

Physicochemical approach to the theory of foam drainage

M. Durand and D. Langevin

Laboratoire de Physique des Solides, Bâtiment 510, Université Paris Sud, 91405 Orsay Cedex, France


(Received 26 June 2001)

We have investigated theoretically the effect of surface viscoelasticity on the drainage of an aqueous foam. Former theories consider that the flow in Plateau borders is either Poiseuille flow or plug-flow. In the last case, the dissipation is attributed to flow in the nodes connecting Plateau borders. Although we do not include this dissipation in our model, we obtain a drainage equation that includes terms equivalent to those of the earlier models. We show that when the water solubility of the surfactant stabilizing the foam is low, the control parameter M for the transition between the two regimes is the ratio $\frac{\mu D_\ab{s}}{\varepsilon R}$, where $\mu $ is the bulk viscosity, $D_\ab{s}$ the surface diffusion coefficient, R the radius of curvature of the Plateau border and $\varepsilon $ the surface elasticity. When the surfactant is more soluble M is rather related to the bulk diffusion coefficient. Within the frame of this approach and in view of the estimated M values, we show that the flow in Plateau borders is Poiseuille-like.

47.60.+i - Flow in ducts, channels, nozzles, and conduits.
82.70.Rr - Aerosols and foams.
68.03.Kn - Dynamics (capillary waves).

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002