Adsorption, Diffusion and Chemical Reaction in a Slab

position in slab

0.2

rate constant k

0.2

c

A

at interfaces

1.

reaction order n

1

diffusivity

0.0025

time

30

This Demonstration considers the adsorption and diffusion of a substance that undergoes an irreversible chemical reaction while traversing a rectangular slab.

The equations describing this system for the reaction

A

k

→

B

are:

∂

c

A

∂t

=

2

∂

c

A

∂

2

z

-k

n

c

A

,

∂

c

B

∂t

=

2

∂

c

B

∂

2

z

+k

n

c

A

,

with the following initial and boundary conditions:

c

A

(0,z)=

c

B

(0,z)=0

,

c

A

(t,0)=

c

A

(t,L)=

c

0

,

c

B

(t,0)=

c

B

(t,L)=0

,

where

c

A

and

c

B

are the concentrations of the adsorbed and product components, respectively,

t

is time,

z

represents the coordinate along the thickness of the slab,

L

is the thickness of the slab,



is the diffusion coefficient,

k

is the reaction constant,

n

stands for the order of reaction with respect to component

A

, and

c

0

is the concentration of component

A

at both sides of the slab.