Biomedical Engineering Reference
In-Depth Information
microfluidic entity with a convex interface. If the inertia forces are progressively
increased, the interface is first deformed by waves, becomes locally concave, and is
finally disrupted [11].
The Ohnesorge number relates the viscous and surface tension forces. It is de-
fined as
η
ργ
We
Oh
=
=
L
Re
(1.12)
The Ohnesorge number has been shown to be a good criterion to predict the breakup
of liquid jets in a gas [12]. Another expression—seldom used—for the comparison
of viscous and surface tension forces is the Laplace number defined by
2
La Oh
(1.13)
In terms of characteristic times, the different dimensionless numbers can be derived
from the characteristic times defined in Section 1.4.2 (see also Figure 1.4). This
schematic diagram brings a new light on the different roles of these dimensionless
numbers in fluid dynamics.
=
1
1.4.4
Non-NewtonianFluids
As soon as the viscosity of a fluid does not depend only on temperature and con-
centration but also on the internal stress, the fluid is categorized as non-Newtonian.
In biotechnology, such fluids are principally polymers (alginate, xanthan) or body
fluids. Their viscosity decreases with an increase of the shear rate. These fluids are
said to be viscoelastic, or shear-thinning.
Figure1.4
Hydrodynamic dimensionless numbers for Newtonian fluids based on the different char-
acteristic times.
