Biomedical Engineering Reference
In-Depth Information
where
C
p
is the specific heat (in J/kg/K),
k
is the conduction coefficient (in W/m/K)
and
q
is a source or sink term (in W/m
3
).
2.2.2 Non-Newtonian Rheology
Usual liquids have a viscosity
m
depending on the temperature
T
and, to a lesser
extent, on the pressure
P
because pressure is most of the time close to atmospheric
pressure in microsystems. If nano- or microparticles are transported by the fluid,
their concentration
c
has an important influence on the viscosity. The general ex-
pression of the viscosity is
(
)
(2.14)
µ
=
f P T c
,
,
This general category of fluids is called Newtonian. Some liquids are more com-
plex, such as polymeric solutions.
2.2.2.1
Introduction
The recent developments of microfluidic systems for biotechnology have widened
the field of applications to more complex fluids like polymeric solutions and body
fluids. Blood is one example. When flowing inside the human body, blood behaves
like a viscoelastic non-Newtonian fluid, which viscosity decreases in high shear-
rate regions, for instance, the vicinity of the walls of arteries, veins, and capillaries
[3]. This property explains why the heart manages to push this very viscous fluid
through the whole body. Ex vivo, blood is most of the time diluted to be handled
by fluidic systems. However, it is a very large gain in time if whole blood can be
manipulated without dilution. Hence, the non-Newtonian character has to be taken
into account in the conception of such systems [4].
Concentrated polymer solutions are another example of non-Newtonian fluid
in microsystems. Agarose and alginate solutions are now being used to encapsulate
living objects like bacteria, cells, and cluster of cells [5, 6]. The principle of such
devices is shown in Figure 2.8. Depending on the concentration, alginate solutions
show a more or less pronounced non-Newtonian behavior [7]. In the following
Figure 2.8
Principleofencapsulationinalginate:dropletsofalginateareirstformedintheFFD,
andthenthedropletsarepolymerizedbythecalciumionstoformcapsules.
