Direct-shadow optics

For such systems bounded by solid surfaces there has been good agreement between experiment and theory. A striking confirmation was achieved in 1935 by Schmidt and Milverton (S4), who studied the stability of a water layer confined between horizontal metal plates spaced from 4 to 5.5 mm apart, measuring the rate of heat transfer across the liquid layer as a function of temperature difference between the two plates. As described earlier, these authors noted an abrupt change in the heat-transfer coefficient at a Rayleigh number of 1770 140, which compares favorably with the theoretical value of 1709. These results were further confirmed using a direct-shadow optical technique. 

Since there are no flat surfaces in the foam borders and vertexes, the entire incident light changes its initial direction, similarly to the case of a spherical bubble. Thus, the optical cross section of borders and vertexes will equal the projection area of these structural elements on a plane perpendicular to the light beam direction (shadow area). 

Benard employed two variations of the direct-shadow method, using reflected light to obtain photographs of free-surface relief during convection. In particular because the free surfaces of his convection cells were essentially basins separated by ridges, from the optical standpoint they simulated concave mirrors separated by cylindrical convex mirrors. By adjusting the position of the viewing screen, as shown in Fig. 12, the cell centers could be... 

Other optical methods include the shadow-optical method of caustics based on the deflection of light by the elastic-stress fleld around the crack tip. It gives direct information on the stress-intensity factor or the strain-energy release rate (21). 

The term Qsh is the net solar radiant energy absorption rate on the basin bottom. It is equivalent to total radiation incident on the basin cover minus reflection from the cover, the water surface, and the basin bottom, and minus loss due to structural shadowing. Its determination from Weather Bureau records of total daily radiation on a horizontal surface is complicated by many factors such as variation in angle of incidence, and resulting transmissivity of cover, hourly and seasonally, intensity change due to cloudiness, and different properties of direct and diffuse radiations. Detailed explanation of these meteorological and optical calculations is beyond the scope of this paper, but may be found in the literature (6). 

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