Dynamic surface tension of detergent solutions at constant and variable surface area

An exact mathematical formulation of the time dependence of the surface tension γ after formation of a fresh surface with constant area has been given by Ward and Tordai (1). The rather laborious calculations are considerably simplified when dealing with detergents obeying the v. Szyskowski equation for the dependence of equilibrium surface tension on concentration. This equation holds for certain non-ionic ethylene oxide compounds. With such detergents it was found that the surface tension—time curves are well fitted by the Ward and Tordai relation. Hence one can conclude that the establishment of the adsorption equilibrium is governed by the diffusion in an undisturbed layer.

When by a rapid expansion or compression of the surface a transient increase or decrease of γ as compared to the equilibrium value γ_∞ is provoked the rate of diminishing or rising of γ during the subsequent reestablishment of the equilibrium for a given detergent solution is dependent not only on the actual deviation of γ from the equilibrium value γ_∞ but also on the preparation (prehistory). This observation can be explained by properties of the diffusion layer and complicates the treatment of surface rheology of detergent solutions.