Simple Reaction with Segregation in a Batch Reactor
Simple Reaction with Segregation in a Batch Reactor
Consider a simple chemical reaction in a batch reactor. The reaction rate in terms of the intensity of mixing, , is given by: ==kI, where and are the instantaneous concentrations, and are the mean concentrations, and and are the initial concentrations of species and . The governing equation is the following:
A+B→C
I

r
A
c
A
c
B

c
A

c
B

c
A0

c
B0
c
A
c
B

c
A

c
B

c
A0

c
B0
A
B
d()

c
A
dt

r
A
This equation can be written in dimensionless form as:
dy
dθ
D
a
η=

c
B0

c
A0
θ=
t
τ
m
τ
m
y=

c
A

c
A0
D
a

c
A0
τ
m
I=

t
τ
m
e
This Demonstration displays the dimensionless concentration versus the dimensionless time for various values of the Damköhler number and the initial concentration ratio. It is straightforward to see that the steadystate dimensionless concentration is independent of the Damköhler number. The Damköhler number has an influence only on how fast this steadystate dimensionless concentration is reached. This steadystate dimensionless concentration is equal to =1η. When →∞, there is an analytical expression for the dimensionless concentration, which is given by:
y
ss
D
a
y
∞
(η1)++4ηI
2
(η1)
2
I=
θ
e