Critical thickness of thin liquid films: Theory and experiment

Abstract

A new theory of the critical state of the thin liquid film, at which it either ruptures or forms a black spot, is propounded. The concept of the spontaneous growth of the surface fluctuational waves at the critical state, proposed by A. Scheludko [ Proc. K. Ned. Akad. Wet. Ser. B 65, 76 and 87 (1962)], is employed. The consistent application of the Brownian motion theory infers that the rate-determining process is that of attaining the state of instability and not, as assumed by A. Vrij [ Disc. Faraday Soc. 42, 23 (1966)], the consequent evolution of the instability. The theory is confirmed by new experimental data on the critical thickness of formation of black spots in films from aqueous solutions of sodium dodecyl sulfate + NaCl. In contrast to the previous studies [E. Manev, A. Scheludko, and D. Exerowa, Colloid Polym. Soc. 252, 586 (1974); A. Scheludko, loc cit.] where the mean critical thickness of the films is determined, in the present study the thickness in the thinnest part of the critical film is measured. In the same manner the rate of thinning at the critical state is obtained. The agreement of experiment with theory confirms the estimate of the van der Waals-Hamaker function according to Lifshitz's theory.