This equation relates to the equation for the integral diffusion coefficient, D, 

 described by Stamm and Nelson (1961) and Stamm (1964). In turn, Stamm states this 

 resulted from Pick's general diffusion equation. 



Stamm' s equation for the integral diffusion coefficient can be rearranged to a 

 form similar to equation (3) : 



D = - ^ 4 (4) 



16 t 



where 



E = fraction of total change accomplished 



a = R = thickness, cm 



t = time for change accomplished 



7T = 3.1416. 



Rearrangement and common defining of terms lead to: 



ttE^ _ vt_ 

 16 " R2 



where the right-hand side is the same as the right-hand side of equation (3) except t 

 is the time for the fraction of the total change, E, instead of 1/A or x, which is the 

 timelag. Since the timelags for the data reported in this paper were calculated from 

 the time for 95 percent of the total change, the diffusivity of the particles and the 

 litter beds can be determined for the same conditions using equation (5) : 



_ TrE2 R2 _ tt (0-95)2 R2 _ r2 _ 



V - — ^ — - 0.177 — (6) 



2 



The quantity, ttE /16, of equations (4), (5), and (6) is a form of the Fourier number. 

 With E equal to 95 percent of the total, the product is 0.177. This value agrees 

 closely with values calculated from figure 2 of Fosberg's 1970 paper on drying rates of 

 heartwood. If we could accurately determine when the total change has occurred, the 

 value should approach 0.1963, tt/16. 



A summary of the timelags, thicknesses, and dif fusivities is given in table 3. 

 The range of dif fusivities is shown in figure 10 which shows the dif fusivities of the 

 particles, the litter beds, and the voids. Both desorption and adsorption diffusivity 

 changes with time are shown and indicate a common diffusivity is approached by both 

 sorption processes. The dif fusivities calculated using three timelag periods and 95 

 percent of the total change are slightly lower than diffusivities computed from specific 

 fractions of total change and the time for the change. However, the differences do not 

 appear significant. 



The diffusivity of the voids was calculated from the diffusivity of free air at 

 the test conditions and considering the porosity of the litter beds. The free air 

 diffusivity was determined by the empirical equation used by Stamm and Nelson (1961) : 



V 







where 



T = temperature, °K 



P = pressure, mm Hg = 760 EXP [-(gh)/(RT )] (8) 



g = 981 cm/s^ 



h = elevation, cm 



R = gas constant for air, 2.87 x lo^ "q^ 



g - K 



Tn, = temperature at test, 300° K. 



17 



