DIFFUSION THROUGH SEFTA 913 



evaporation from an extended surface is proportional to its area, while the 

 amount of evaporation from a small sphere is proportional to its radius; 

 the same applies to the comparison of diffusion across an extended plane 

 (the case usually considered in the derivation of diffusion equations) with 

 the diffusion through a small hole. Diffusion through a multiperforated 

 septum can be treated in the same way as that through a single hole as long 

 as the distance between the holes is large enough (compared with the radius 

 of the holes) for the half-spherical surfaces of equal concentration (and the 

 radial lines of flow, which are normal to these surfaces) to be established 

 around each hole without marked interference by the neighboring holes. 



This principle was first applied to the penetration of carbon dioxide 

 through the stomata by Brown and Escombe (1900) upon advice of the 

 physicist Larmor. Renner (1910, 1911), Brown (1918), Freeman (1920), 

 Sierp and Noack (1921), Sierp and Seybold (1927, 1928, 1929), Huber 

 (1928) continued the study, being, however, mainly concerned with the 

 trans-piraiion of plants. As a typical result, we reproduce a table from 

 the paper by Sierp and Seybold (1929). Table 27.11 shows the rates of 

 evaporation of water through septa with different numbers of holes but a 

 constant total open area. The next-to-last row shows the flow-retarding 

 effect of an inadequate distance between the holes. The table indicates 

 that a maximum rate of diffusion is reached asymptotically when the holes 

 are reduced to 20-10 n in diameter. Although the aggregate area of the 

 holes (3.14 mm.2) is less than 1% of the total area of the vessel (-400 mm.^), 

 the evaporation rate through the septum with holes 10 n in diameter is as 

 high as 70% of that from the open vessel. These figures indicate that the 

 dimensions of the stomata (5-15 n) may be appropriate to ensure the de- 

 sired rate of gas exchange through the smallest possible number of openings. 



Table 27.11 

 Evaporation through Septa (After Sierp and Seybold 1929) 



The theorj^ of gas diffusion through multiperforate septa was further 

 advanced by Verduin (1949), by mathematical analysis of the mutual 



