Time-Dependence of Boundary Tensions of Solutions I. The Role of Diffusion in Time-Effects

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Abstract
The variation of surface tension of solutions with time has in some cases, where the change is over within a few seconds or less, been explained on the basis of diffusion. This paper attempts a rigorous mathematical analysis of the role that diffusion might play in such time-effects. The limitations of diffusion theories which have been proposed previously are discussed. A general theory of diffusion to the surface is derived, which allows for back-diffusion and which makes no special assumptions of a physical nature. It is possible to use Fick's equation to calculate the total amount of solute which diffuses from a semi-infinite bulk solution into the surface if the concentration immediately under the surface is known at various times throughout the process. It is shown how the latter information may be deduced from the variation of surface tension with time together with final equilibrium values of surface tension. The methods of this theory are applied to analyze recent data on time-effects of short duration. It is concluded that even in cases where the variation of the surface tension is over in less than a second the rate-determining process is not diffusion. Even for these very rapid changes one is therefore led to assume the existence of an activation barrier which determines the rate of adsorption.