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simulated data for 2.0 mm outer diameter nodules at four different barrier permeabilities where P is calculated as
P = D S / Lx (4.9)
where S is the solubility of acetylene in the cytoplasm (assumed to be
1.0), and Lx is the thickness of the diffusion barrier (mm).
Except for the the initial few seconds of the simulation each of these curves appear to be exponential in nature and to fit the general exponential equation
-t/tu
F = Ffin (1 e ) (4.10) e fin
3 -1
where F is the ethylene out flow (mm s ) from the chamber at time t
e
3 -1
(s), F in is the final steady-state ethylene out flow rate (nrm s ), and tu is the associated time constant (s). Equation 4.10 can be transformed to a linear equation such that
In(l F /F ) = -(l/tu) t (4.11) e fin
where In is the natural logarithm. Equation 4.11 describes a straight line with slope -(1/tu). Thus a simple linear regression can be used to find the time constant (tu) associated with the simulated data sets for each nodule size and permeability. Figure 4.4 is the same data presented in Fig. 4.3 which has been transformed according to Equation
4.11. The data from each of the simulations was transformed in this