Kinetics of Surfactant Adsorption in Foam Films

Equation of dynamics of the adsorption layer. In the case of foams, the main interface consists of films in which the liquid is virtually stagnant. The film surface is even more constrained. Therefore, Eq. (7.3.1) describes the molecular (or Brownian) diffusion in the bulk of liquid, and Eq. (7.3.2), under the additional assumption that the specific adsorption is rapidly smoothed along the interface (i.e., T = r(t)), describes the dynamics of a localized (or ideal) adsorption layer [119, 250,511]  

The value Cs is the instantaneous local concentration of surfactants on the boundary of the foam film. Note that the last term in Eq. (7.3.7) originates [250,415] from the term containing the divergence of the surface velocity in Eq. (7.3.2). 

Dynamics of the adsorption layer for the foam film. Taking into account the fact that in actual foam of high multiplicity the film thickness h usually does not exceed 10 micrometers, the time td = h2/D of diffusion relaxation in the film is a fraction of a second, and hence the concentration is equalized throughout the film thickness almost instantaneously. For this reason, we can omit the subscripts S on Cs indicating the corresponding surface and assume that 

One can assume that C - const and S - const at the boundary of the surfactant solution. In this case, we can find the solution of Eqs. (7.3.7), (7.3.8) in the form 

We must point out that if the adsorption layer contacts with a sufficiently deep liquid, then the diffusion relaxation time can be comparable with the adsorption relaxation time. In this case, the kinetics of the adsorption layer filling, which is determined by Eqs. (7.3.3) and (7.3.4), can be diffusion-controllable for small volume concentrations of surfactants in the solution or be governed by a diffusion-kinetic mechanism for higher concentrations [274]. A pure kinetic region of the adsorption layer filling is possible only in thin layers of surfactant solutions, for example, in liquid elements of foam structures. 

---