Kinetics of Spreading Processes

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it , although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

The topic of spreading rates is of importance in the technology of the use of mono-layers for evaporation control (see Section IV-6) it is also important, in the opposite sense, in the lubrication of fine bearings, as in watches, where it is necessary that the small drop of oil remain in place and not be dissipated by spreading. Zisman and coworkers have found that spreading rates can be enhanced or reduced by the presence of small amounts of impurities in particular, strongly adsorbed surfactants can form a film over which the oil will not spread [48]. 

A familiar (and biblical [SO]) example is the formation of tears of wine in a glass. Here, the evaporation of the alcohol from the meniscus leads to a local raising of the surface tension, which, in turn, induces a surface and accompanying bulk flow upward. 

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. 

---