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. LangevinLaboratoire de Physique des Solides, Bâtiment 510, Université Paris Sud, 91405 Orsay Cedex, France mdurand@lps.u-psud.fr
(Received 26 June 2001)
Abstract
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
, where
is the bulk viscosity,
the surface diffusion coefficient,
R
the radius of curvature of the Plateau border and
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