Surface Tension Gradients and Foam Film Stability

1 Surface Tension Gradients and Foam Film Stability 

FIGURE 1.4 Limiting range of velocity profiles in draining foam film, (a) Plug flow, (b) Flow with parabolic velocity profile when film surfaces are immobile. Arrows represent magnitude of fluid velocities My in the y direction. 

we find that if the force of gravity is to be resisted by the film, then a surface tension gradient must exist at the air-liquid surface. Combining the relevant Navier-Stokes equation with Equation 1.1 as a boundary condition, Lucassen [15] shows that in the case of a vertical film in the gravity field the gradient is 

Surface tension gradients due to differences in the surface excess of soluble surface-active components may exist only when either the surface is not in equilibrium with the bulk composition or there are concomitant differences in bulk composition parallel to the surface. In the case of the former, the magnitudes of the gradients are of course determined by the rate of transport of surfactant to the relevant surfaces. With concentrated surfactant solutions, transport rates by diffusion will be rapid and surface tension gradients will be diminished so that shear rates are only balanced at 

Differences in bulk composition are possible in a thin foam film as a result of stretching of the film. If the film is sufficiently thin, then any stretching causes a depletion of the bulk phase surfactant solution between the air-liquid surfaces of the foam film as more surfactant adsorbs on those surfaces. Distances perpendicular to the film are small so that, provided the stretching occurs reasonably slowly, the equilibrium inside the film element may be always maintained. Depletion of bulk phase the surfactant concentration will therefore necessarily mean an increase of the surface tension of the film as it is stretched. This will, however, only occur if reduction of the surfactant concentration causes a concomitant increase in surface tension. In the case of a pure surfactant at concentrations above the critical micelle concentration (CMC), this may not always happen. 

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