Motion of foam films in diverging-converging channels.

Existing theories of the motion of foam films in capillaries often assimilate the pressure drop over the foam films to the static capillary pressure obtained from the Young-Laplace equation. Hence, they ignore the contribution of dynamic effects associated with the rapid stretching and contraction of the foam films to the overall viscous dissipation. This paper reports an investigation of the motion of foam films in axisymmetric diverging-converging channels, taking into account surface viscosity and elasticity. First, a phenomenological theory for the motion of the foam films is developed using simple physical arguments. We show that the displacement of the film obeys a nonlinear second-order differential equation, which can be solved numerically for the (dimensionless) distance from the inlet and the pressure drop as a function of time. Experiments with foam film motion, conducted using glass diverging-converging channels (minimum radius = 3.00 +/- 0,01 mm, maximum diameter = 7,98 +/- 0,01 mm) and nitrogen foam stabilized with sodium dodecyl sulfate (SDS) in brine, are discussed. For a single film motion in the diverging channel, we find that (a) the static pressure drop is a concave-upward function of distance and decreases from 1.0 to about 0.3, whereas (b) the dynamic pressure drop is concave downward and increases from 1 to a maximum of 1.3 and then decreases to 0.7. In the converging channel both the static and dynamic pressure drops are concave-downward functions, but the dynamic pressure drop values are always higher than the static ones. For two films the motions were found to be rather sensitive to the initial arrangement in the channel. The experiments are found to be in excellent agreement with the theoretical predictions. These observations imply that the large flow resistance obtained during foam flow in granular porous media, where converging-diverging channels are abundant, is largely due to the surface elasticity and viscosity of the films.

Effect of foam films on gas diffusion.

We report an experimental investigation of the permeability to gas of systems of one or several soap films freely standing in a straight tube, using either reactive gas (NH(3)) or inert gas (argon). The series of soap films appears to be the simplest paradigm of successive lamellae arrangements encountered in foams confined in a porous medium. To conduct the experiments, we devised two novel methods for the determination of gas diffusion fluxes: one based on reactive changes of pH by NH(3) and the other on mass spectrometry. The permeability of a single film, stabilized by sodium dodecyl sulfate solution, was found to be 3.50+/-0.04 10(-2) cm/s for argon and 3.18+/-0.07 10(-4) cm/s for NH(3). The permeability value for the inert gas is in good agreement with data obtained by the diminishing-bubble method. When the number of films increases, the permeability decreases considerably as a result of cumulative film resistance effects. We also developed a simple phenomenological model based upon a combination of gas kinetic and energy barrier concepts to interpret our data. This model takes into account gas solubility and the effects of salinity, which have seemingly been ignored in previous models. The predicted film permeability decreases sharply with increase surfactant concentration, indicating the occurrence of higher adsorption and increasingly compact surfactant layers.