In: Other
We want to remove a carcinogenic substance (which of course is
in a small concentration)
from some industrial waste. As an engineer, you have found a
special material in the shape
of a sphere of radius r0, in which the substance diffuses with
diffussivity of D(eff).
Within the sphere, the substance is consumed (is bound) at an
independent rate of its concentration,
i.e. its consumption per unit volume is ko.[ C(A,G)=-Ko]
The concentration of this substance in radious R is Co.
(a) We need to derive the expression for the distribution of the
concentration of the substance in
a sphere from this special material, C(r), with the assumption that
its consumption,
as has been said, is spatially uniform.
(b) Under what conditions is the concentration of the substance in the center of the sphere 0?