Biomedical Engineering Reference
In-Depth Information
Figure 4.64
Sketch of the effect of stretching and folding in the straight parts and reorientation in
the turns.
2
σ
-
2
n
a
(4.92)
t
( )
n
=
diffusion
2
D
On the other hand, if we remark that
d
(1) is of the order of
L
, the convection
time is given by
d n
L
( )
t
n
»
=
n
(4.93)
( )
convection
U
U
Following Bringer et al. [66] and Stroock et al. [68], the mixing time is obtained
by equating the diffusion and convection time, so that
s
2
σ
-
2
n
L
a
(4.94)
t
( )
n
»
n
»
=
t
( )
n
convection
diffusion
U
2
D
After rearrangement, we find
aU a
a
2
n
2
n
σ
»
»
Pe
(4.95)
D L
L
where
Pe
=
aU/D
is the Peclet number. Equation (4.95) produces the value of
n
(number of segments) necessary to obtain mixing. If we remark that the solution of
Figure 4.65
Baker's transformation and reduction of the striation length.
