Theories of Film Elasticity

Theories concerning the mechanisms of operation of this film elasticity depend on two observations concerning the surface tension of aqueous solutions of surface-active solutes (1) its increase in value with decrease in concentration of the surface-active solute, at concentrations of the latter below the CMC, and (2) the time required for it to obtain its equilibrium value (the fact that the initial value of these surface tension at a new surface is always greater than the equilibrium 

FIGURE 7-2 Stretched portion of foam lamella, illustrating the mechanism of Him elasticity. 

The Marangoni effect is signihcant only in dilute solution and within a limited concentration range. The amount of solute adsorbed at a new surface in the absence of stirring or an energy barrier to adsorption is given by (Ward, 1946) 

D = bulk diffusion, coefficient cm2/s, c = bulk concentration, in mol/L, t = time, in seconds, 

The times involved in foam production are in the range of 0.001-0.1 s the value of D/n for the usual surface-active solute (with a hydrocarbon chain of 12-18 carbon atoms) is of the order of 1 x 10-6 cm2/s equilibrium surface concentrations for this same type of material are about 2 x 1014 molecules/cm2. Thus, if the time needed to replace the solute at a new surface is to be no shorter than the time 

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