J. E. Coons

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces.

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Frenkel criterion and is obtained from the zeroth order approximation of the H3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H3 term in the evolution equation and is dependent on the film thinning velocity. A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semi-empirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams.

Compression stress relaxation apparatus for the long-time monitoring of the incremental modulus

A compression apparatus for aging experiments on soft rubbers and foams is presented. The sample is compressed between two parallel surfaces and held there for long-time relaxation studies. The specific purpose of the test is twofold: possible exposure of the sample to aggressive environment under compression during aging and measurement of sample modulus without unloading, i.e., while leaving the sample under constant compression at all times. To determine the restoring force in the compressed sample, the compression strain is modulated with an incremental strain while measuring the force response. The total force gives the compression modulus, and the slope of the force-strain curve allows the determination of the incremental modulus. Stress relaxation data for silicon foam, Dow Corning S-5370 RTV, with 68% void fraction are shown. The modulus of the compressed sample decays over long experimental times of several days. The decay can be described by two relaxation modes, a short mode at 1500 s and a lon...