Biomedical Engineering Reference
In-Depth Information
Snapshot of the three-dimensional network structure produced from simulated aggregation of
particles with
ϕ
= 0.05, no interactions. The darkest particles lie furthest away from the observer.
Bijsterbosch and Bos (
1995
) introduced a scaling factor n
0
for the average number n(r) of particles
within a range r of another particle. Here n
0
= 0.5. Particles can form irreversible flexible linkages
with other particles when they approach to within a certain bonding distance. Assuming a bond
probability of 1, at low volume fractions the simulation produces a fine-stranded network structure
having a
fine-pore distribution. Reproduced with permission of the Royal Society of Chemistry.
Figure 2.21
Ultimately, the overall microstructure is likely to be dependent on the volume fraction
of particles and on the detailed nature of the particle
particle interactions during and after
phase separation. In such simulations, when the volume fraction of systems reaches
ϕ
-
= 0.3 or above, no fractal character can be found.
2.6.2
Gelling or non-gelling systems?
The method developed by Lodge and Heyes allows the computation of linear rheological
properties without any assumption about the microstructure and without applying a shear
strain to the system but, instead, attributing a purely thermodynamic origin to each
instantaneous con
guration (Lodge and Heyes,
1999a
). In this model, rheological proper-
ties, purely thermodynamic in origin, are computed from the stress tensor elements. The
stress relaxation function, which contains a complete description of the linear response
viscoelasticity (G
0
(
)andG
00
(
)), relaxes to zero in the stable single phase. In the phase
separated system, it does not relax to zero but reaches an apparent plateau within a certain
time interval, of the order of several tens of a
2
/D
0
, where the structure does not change
appreciably, so suggesting the presence of an elastic network. The residual stress can be
ω
ω
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