Reaction-Diffusion Equations for an Autocatalytic Reaction

time t

1

diffusivity δ

10

rate constant ρ

10

This Demonstration shows the behavior of a reaction-diffusion system in which an autocatalytic reaction takes place.

Consider the reaction scheme

A+B2B

with rate of reaction

r=ρ

C

A

2

C

B

, where

C

A

and

C

B

are the reactant concentrations and

ρ

is the reaction rate constant. The reaction takes place in a capillary tube of length

2L

filled with a fluid separated by an impermeable membrane. Half of the tube's length contains reactant

A

and the other half contains reactant

B

. The membrane is removed at time

t=0

and the reaction-diffusion process begins. The plots of functions

C

A

and

C

B

are shown for user-selected values of time

t

, diffusivity

δ

, and reaction rate constant

ρ

.