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Liquid

Vapor

Fig. 1 Temperature-enthalpy diagram of water.

thermally stored enthalpy into useful work. I can vividly present these concepts in terms of the T-S diagram for water, Fig. 1. To the left of the T-S curve water is a liquid, to the right it is a vapor. Below the T-S curve the water is a mixture of liquid and vapor. I now address the following question. Suppose we have a large heat reservoir at a subambient temperature, say 40 °F. Near this reservoir we have a supply of room temperature water, namely 80 °F. How can we take advantage of the higher enthalpy of this 80 °F water to obtain power without having to employ expensive heat exchangers? Our answer to this question was to establish a rising foam column. This we would do by feeding into the column our 80° F water in the form of a close packed array of bubbles at the saturation vapor pressure of 80° F water. As an element of this close packed array rises, several changes take place simultaneously: the pressure drops, the temperature also drops, evaporation takes place, the foam cells expand. In the absence of losses, the foam will rise 960 feet before the pressure drops to the saturation pressure of the 40 °F water.

If we break the foam at this height, the freed vapor can be conducted back to the ground level, there to be condensed by a spray of 40"F water. The water from the broken foam is collected into a pipe, which in turn feeds it into a hydraulic turbine at ground level, thereby providing a 960 foot head. The practical application we have in mind is for the Gulf of Mexico or other tropical ocean water. Here the top mixed layer of 200 feet depth is our pool of 80 °F water. The cold deep water provides the 40 ° F reservoir. A remarkable feature of foam is its mechanical temporary stability. This stability requires, however, a small quantity of surfactant. In order to understand the role played by surfactants, consider one foam cell, Fig. 2. Each of the six corners is bounded by convex boundaries. Because of their surface tension, convex boundaries produce a lower pressure inside the corners than in the vapor. However, the pressure between the flat walls is identical to the pressure in the surrounding vapor. The pressure within the corners is therefore less thar the pressure within the walls. In the absence of intervening forces, the corners would therefore spontaneously

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AQUEOUS FOAMS 1

,,ull the walls apart. Willard Gibbs pointed out in the 1870s that an intervening force is provided by molecules that are repelled from the interior of the water onto the surface. These molecules are now called surfactants. Solute molecules in the interior of water exert a pressure, called osmotic pressure, which is numerically equal to the pressure they would exert on the walls of a