51
3 -3
has been completed and is assumed to be 0.10 mm mm t is the time elapsed since acetylene was introduced to the chamber (s), and tau is the chamber time constant assumed to be 2 sec.
Since the assumed thickness of the diffusion barrier (10 to 70
micrometers) is small compared to the diameter of the sphere (1.48 tc
2.38 mm), diffusion across the barrier can be modeled with slab geometry. To do this the barrier was divided into compartments 1.25 micrometers in width and the diffusion of acetylene and ethylene across these compartments was modeled with a continuity equation such that
dc/dt = (flow. flow + generation) / vol. (4.6) in out I
where dc/dt is the change in concentration of the diffusing gas with
3 -3 -1
time (mm mm s ), flown and flowout are the flow rate of the gas
3 -1
into and out of the compartment respectively (mm s ), generation is
3 -1
the rate of generation of the gas in the compartment (mm s ), and vol.
I
is the compartmental volume (mm3). Since ethylene is not generated in the diffusion barrier, Equation 4.6 can be used to describe the inward diffusion of acetylene such that
dCa./dt = D (Ca.i+ 2*Ca. + Cai-) / (1.25 10-3 ) (4.7)
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where Ca. is the concentration of acetylene (mm mm ) in the ith
1
compartment (with i=O at the outer edge of the barrier), and D is the
2 -1
diffusivity (mm s ) of acetylene in the compartment. Once the