50
the time to steady-state, numerical methods must be employed. To do this a series of nodules were simulated in order to generate a table of predicted times-to-steady-state for nodules of various dimensions and with different values of P.
Simulated nodules were assumed to be spherical and to have outer diameters of 2.0, 2.5 and 3.0 mm. The corresponding diameters of the nitrogen fixing inner zone for each of these nodule sizes were calculated according to Bergersen (1982) as being 1.48, 1.84 and 2.38 mm, respectively. Thicknesses used for the diffusion barrier were 10, 20, 30, 40, 50, 60 and 70 micrometers, and the value of the diffusivity of acetylene and ethylene was calculated from published values for 02 diffusivity in plant tissues (Berry and Norris, 1949; Dungey and Pinfield, 1980) which were extrapolated to 26oC (Carlson, 1911) as
-4 2 -1
4.6*10 mm s The solubility of acetylene was assumed to be 1.C and that of ethylene to be 0.108 (Orcutt and Seevers, 1937). These assumed
-3
values resulted in simulated values of P which ranged from 6.57*10 to
-2 -1
4.60*10 mm s .
If the time constant of the assay chamber is known, and if perfect mixing occurs in the chamber then the acetylene concentration at the outer surface of the nodule can be modeled as
A A (1 et/tau (4.5) ex fin
where Aex is the concentration of acetylene in the assay chamber and at
3 -3
the outer most surface of the diffusion barrier (mm3 mm ), Afin is the fin
final concentration of acetylene in the chamber (mm3 mm-3) after mixing