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summaryDilute macromolecular solutions often exhibit flow characteristics which are remarkably different from those of the Newtonian solvent. Drag may be decreased in turbulent shear flow and increased in flow around cylinders and through porous media. In dilute polymer solutions turbulent clouds will disperse more slowly, jets become more stable, and Taylor and bath-tub vortices may be supressed.Some of these effects may be explained by assuming the macromolecules stretch in strong flows. But often the effects occur in weak flows or flows in which substantial stretching is incompatible with the kinematics, and further the onset of the non-Newtonian behaviour often depends on polymer concentration.It is proposed here that "fresh" solutions of macromolecules are heterogeneous. When dilute solutions are prepared from concentrated master solutions, strings are created by the mixing process and these strings form a network in the fluid. The difficulty in obtaining repeatable experimental results, as well as the disappearance of many non-Newtonian effects in aged solutions which retain drag reducing ability in turbulent shear flow, may be explained by this model.If the strings of polymer solutions are sufficiently long compared with their thickness, the network will move with the surrounding fluid. At low rates of strain a dilute network will hardly affect the solvent properties. Under high rates of strain, of sufficient duration, strain hardening will cause * Presented at the IUTAM Symposium on Non-Newtonian Fluid Mechanics, Louvain-la-Neuve, Belgium, 28 August-l September, 1978. ** On leave from Ben Gurion University of the Negev, Israel. 412the elasticity of the strings to predominate; the fluid will behave like a concentrated polymer solution with "diluted" elastic properties. The similarity of the kinematics of concentrated and dilute solutions could be explained by such a liquid network model. Rheological equations may be easily contructed for such polymer solution networks if those of the concentrated "master" solutions are known. Many rheological equations for concentrated polymer solutions are, however, found to have some deficiencies when the liquid network model is applied to the sink flow through an orifice.

The formation of spray through flashing, from containers pressurized by volatile propellants dissolved into the spray liquid, is studied. A model for the flashing process is proposed. While the pressurized solution is discharged from the container into the atmosphere, vapor bubbles are produced. These bubbles grow rapidly through evaporation of the propellant. When they touch each other, flashing is assumed to occur-the bubbles "explode" and an aerosol is formed. The energy contained in these exploding bubbles is, in part, transformed into surface energy of the droplets of the aerosol. On the basis of this model of the flashing process, a mathematical derivation is presented, expressing the average spray droplet diameter in terms of the physical properties of the binary fluid system. An experimental program was carried out in which the droplet size distribution of an aerosol generated by a flashing process was measured. The average droplet diameter was correlated with the pressure in the container and with the relative concentration of the propellant in the mixture. Experiments were carried out at different temperatures. Comparing the experimental results with the proposed theory, it was found that deviations from the thermodynamic equilibrium have to be taken into account. Doing so, incorporating deviations from equilibrium for water vapor, the experimental data fitted the theoretical prediction for the average drop size quite well over the range of experimental pressures and temperatures.

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