Self-motion Surface tension

Suppose that a is sufficiently small, i.e., We is sufficiently large, that surface tension plays no role in determining the bubble shape, except possibly locally in the vicinity of the rim where the spherical upper surface and the flat lower surface meet. Further, suppose that the Reynolds number is sufficiently large that the motion of the liquid can be approximated to a first approximation, by means of the potential-flow theory. Denote the radius of curvature at the nose of the bubble as R(dX 6 = 0). Show that a self-consistency condition for existence of a spherical shape with radius R in the vicinity of the stagnation point, 0 = 0, is that the velocity of rise of the bubble is... 

Film stability. The formation of y-gradients is all that allows stable liquid films to be made. A film of pure water immediately breaks. To be sure, a thin film is never stable in the thermodynamic sense, but its lifetime can be quite long if it contains surfactant. Figure 10.29c illustrates the so-called Gibbs mechanism for film stability. If for some reason a thin spot forms in a film, this implies a local increase in surface area, hence a local decrease in surface load, hence a local increase in surface tension, hence motion of the film surfaces in the direction of the thin spot, hence a Marangoni effect, i.e., flow of liquid toward the thin spot, hence a self-stabilizing mechanism. Actually, a more elaborate treatment of film stability is needed (see Section 13.4.1), but the Gibbs mechanism is essential. 

Surface self-diffusion is the two-dimensional analogue of the Brownian motion of molecules in a liquid bulk. Measurements of self-diffusion have to be performed in complete absence of any Marangoni flow caused by surface tension differences. Such experimental conditions are best established in an insoluble monolayer where one part consists of unlabelled and the other of radio-tracer labelled molecules. The movement of molecules within the surface monolayer can be now observed by using a Geiger-Miiller counter. There are possible effects of liquid convective flow in the sublayer which was discussed for example by Vollhardt et al. (1980a). With e special designed apparatus Vollhardt et al. (1980b) studied the self-difihision of different palmitic and stearic acid and stearyl alcohol and obtained self-diffusion coefficients between l-i-4 lO cm /s. 

NMR chemical shift for the ring protons, as well as for the methyl group protons, will occur at about the MHC and around the concentration where the surface tension levels off. Spin-lattice relaxation measurements also showed a restriction in the molecular motion above the MHC. Both of these observations are indicative of self-association of non-covalent assemblies. A gradual aggregation is suggested since the revalue stays approximately stable as a function of the hydrotrope concentration until the MHC is reached, after which it decreases quite slowly. 

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