Biomedical Engineering Reference
In-Depth Information
Peclet number via a power law. In a typical Levêque problem (see Chapter 6), this
correlation is [20]
1
3
æ
H
ö
Sh
=
1.615
Pe
L
ç
÷
è
ø
where
H
is the channel width and
L
is its length.
SpeciicDimensionlessNumbersandCompositeGroups
Recently, new dimensionless numbers have been introduced to answer new specific
problems. Others have been introduced with the development of complex multi-
physics phenomena. In this section we present some of them, relative to microsys-
tems for biotechnology.
Microdrop impact on liquid or solid surfaces is of great interest for ink-jet
printing and spray cooling. The
K
number has been defined to separate the splash-
ing and spreading regimes. The
K
number is a combination of the Weber and
Ohnesorge numbers [21]
1.4.7
-
2 5
K We Oh
=
(1.27)
A high
K
number value indicates splashing.
In microreactors, the Graetz number estimates the relative importance of dif-
fusion and convection length. For example, in a straight channel, it compares the
mean axial length traveled by a particle/molecule to the mean transverse length
traveled by the particle/molecule. The axial displacement
L
is principally due to
convective transport and the radial length
w
is due to the effect of Brownian diffu-
sion [22], and the Graetz number is
Gr L w
=
(1.28)
In micro-exchanger, the Graetz number is a function of the Peclet number [23].
Figure1.13
Vortices in channel curve enhance mixing at large Dean number. Reprinted with per-
mission from []. Copyright 00 Royal Society of Chemistry.
