Monday, November 26, 2007

The Liquid-Gas Interface; Droplets and Cavities

On the Monday before Thanksgiving break, we applied the concepts of chemical potential to an interesting system, the liquid-gas interface. We first briefly discussed the difference between vaporization and boiling [which occurs only in open systems] before showing how the vapor pressure of a liquid varies as a function of external, applied pressure (due to either mechanical forces or a secondary inert gas present).

We turned our attention away from phase transitions and developed a little further the notion of surface tension, seen before in the differential form of surface work: dw = ╬│da. Surface tension of liquids is a function of intermolecular forces and, for larger molecules, mechanical tangling. Molasses, for example, has enormous surface tension due to the long alkyl chains.

Further, we saw through the Guggenheim-Katayama equation that the surface tension decreases with increasing temperature. This can easily be demonstrated experimentally by looking at the relative ease of floating needles or razor blades on the surface of cold versus hot water.

We can ask ourselves why droplets of water (or other liquids) tend to be spherical, especially in the absence of gravity, a result easily obtained by considering the Helmholtz energy. We can further obtain the Laplace-Young equation which demonstrates that, for a sphere, the pressure inside is always greater than the outside (a result that is general for either droplets or cavities). It is easier, for example, to create large cavities in liquids than small ones (which is why we add boiling stones when we drive off organic solvents -- to prevent such bumping). Large droplets form more easily than small ones, which is why cloud formation typically needs dust particles suspended in the air.

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