Biomedical Engineering Reference
In-Depth Information
Figure 2.53
(a)Sketchoftherecirculationchamber;(b)3DcalculationwithCOMSOL.
top cover). In the literature, one finds mostly active (electric, acoustic, magnetic)
methods [53, 54]. Note that recirculation is facilitated if there is a free surface—and
less friction at the wall. This is the case of an open microbeaker actuated by an ionic
wind needle [55]. However, in some cases, recirculation can be passively achieved
by a careful design of the system.
Next we indicate a rule to achieve recirculation in a microsystem derived from a
computational approach. Let us take the example of a microchamber placed along
a straight channel, such as that of Shelby et al. [52] (Figure 2.53).
It has been experimentally observed that the Reynolds number of the flow is
strongly linked to the occurrence of recirculation [52]. The COMSOL numerical
program has been used to investigate the occurrence of recirculation. Because of
the importance of the friction on the bottom and top walls, a 3D calculation is
necessary. Two main parameters stem from the results: a channel Reynolds number
defined by
V
D
V
max
2
w d
w d
max
H
Re
=
=
(2.95)
ν
ν
+
where
w
and
d
are, respectively, the channel width and depth; and the gating ratio
is defined by
G d h
=
/
(2.96)
where
h
is the opening length of the microchamber. Figure 2.54 shows the recircula-
tion conditions.
On one hand, the Reynolds number must be sufficiently high; on the other
hand, the gating ratio should be sufficiently large (e.g., the depth of the channel
should be large in front of the width of the opening of the microchamber). A very
interesting feature is the assurance to have a recirculation when
d
/
h
> 0.8, even with
a small Reynolds number. However, in this case, the recirculation velocity is quite
small.
2.2.15 Inertial Effects at Medium Reynolds Numbers: Dean Flow
Usually, Reynolds numbers are very small in microsystems for biotechnology, most
of the time smaller than 1, and the flow is highly laminar. However, recently, me-
dium ranges of Reynolds numbers (Re ~ 1 to 20) have been investigated. It has
