Reaction-Diffusion Equations for an Autocatalytic Reaction

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This Demonstration shows the behavior of a reaction-diffusion system in which an autocatalytic reaction takes place.
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Contributed by: Clay Gruesbeck (March 2014)
Open content licensed under CC BY-NC-SA
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Details
The governing equations are
and
.
With the membrane at , the initial conditions are
,
and
,
with boundary conditions
at
and
.
Here
and
are the diffusion coefficients of
and
, respectively,
is distance, and
is time.
The system can be simplified by making the transformations
and
to obtain the system
,
,
which has the following analytical solution when [1]:
,
,
with
, where
is a free parameter taken as
.
Reference
[1] A. H. Salas, L. J. Martinez H., and O. Fernandez S., "Reaction-Diffusion Equations: A Chemical Application," Scientia et Technica, 17(46), 2010 pp. 134–137. www.redalyc.org/pdf/849/84920977041.pdf.
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