Biomedical Engineering Reference
In-Depth Information
the equation
xe
x
= q
is given by the Lambert-W function defined by
xe
x
= q
Þ
x =
W
(
q
), then
n
is given by
æ
a
ö
W
ln
σ
Pe
L
ç
÷
è
ø
(4.96)
n
»
2ln
σ
Suppose now that the flow rate
Q
dis
<
Q
cont
, (4.84) gives
L
~
a
and introduce
the value
s
= 2 of the Lyapunov coefficient. Equation (4.96) becomes
W Pe
(0.7
)
n
»
1.4
Using typical values of
D
~ 10
-9
m
2
/s,
U
~ 1 mm/s and
a
= 100
m
m, the value of
the Peclet number is 100 and
n
~ 3. In the case where
D
~ 10
-10
m
2
/s, the number
of segments required to obtain mixing is 5.
4.4.3 Micro Flow Focusing Devices (MFFD)
4.4.3.1 Introduction
Controlling the size of droplets and their monodispersity is fundamental in bio-
technological applications. Repeatability is needed for the automation of any sys-
tem; however, calibration is required by biologic protocols. A free jet breaks up
somewhat randomly under the effect of the Plateau-Rayleigh instability and gives
birth to polydispersed droplets (Figure 4.66). A T-junction already helps to produce
Figure 4.66
Comparison between jet instability (a), T-junction (b) and FFD (c).
