
255Homogeneous Reactors
where
is the unit impulse function (Dirac delta function). The tracer concentration at
the vessel output
(,
1
θ is the normalised E-curve
θ (Figure 3.75), that is
() (, )
= 1 (C.5)
Dimensionless mean residence time
θ and variance
σ
2
are
() ()
θθθθ
θ
θ
=
∫
Ed
1
(C.6)
and
σθθθ
22
1
∫
Ed()
(C.7)
Dene the Laplace transformation of
(,
B
θ as
Cs LC Ced
s
(,)(,) (,)BB B=
{}
=
−
∫
θ
θ
0
(C.8)
Then
Es LE
() () (,)=
=
θ 1 (C.9)
Taking Laplace transformation of Danckwarts’ model Equation B.1, we get a second-
order ordinary differential equation in ʓ
1
0
2
2
Pe
dC s
d
dC s
d
sC s
(,)(,)
(,)
B
B
B
B
B−−= (C