Biomedical Engineering Reference
In-Depth Information
1
3
2
(
)
De
=
τ γ ρ
R
(1.17)
The smaller the Deborah number, the more fluid the material appears [5].
The elasticity number is the ratio of the Weissenberg number to the Reynolds
number; it represents the ratio of elastic to inertial stresses
Wi
η τ
ρ
0
El
=
=
(1.18)
2
Re
R
The elasticity number does not depend on the process kinematics, only on the fluid
properties and geometry of interest. It can also be seen as the ratio of the relaxation
time
τ
to the diffusional time
R
2
/
v
established in (1.6). For example, extrusion of
polymer melts corresponds to
El
>>1 (Figure 1.6), whereas flow of dilute polymeric
liquids correspond to
El
<<1 [5].
The elastocapillary number characterizes the relative importance of elastic and
capillary effects as compared to viscous stresses
τγ
η
Ec
=
(1.19)
L
0
In terms of characteristic time, it is the ratio of the relaxation time
τ
and the Tomo-
tika time defined in (1.8) by
τ
T
=
η
0
R
/
γ
. Figure 1.7 shows how the different dimen-
sionless numbers for viscoelastic behavior can be deduced from the characteristic
times.
1.4.5
DropletsandDigitalMicroluidics
The Bond number is a measure of the importance of surface tension forces com-
pared to body (gravity) forces. A high Bond number indicates that the system is
relatively unaffected by surface tension effects; a low number indicates that surface
tension dominates (Figure 1.8).
Figure1.6
Elasticity of a liquid alginate filament during droplet formation (the encapsules are Jurkat
cells) (photo CEA-LETI).
