Biomedical Engineering Reference
In-Depth Information
, that deformation occurs in the bulk of the sample,
rather than by de-adherence at the interface. Alternatively the sample surface can be well
lubricated; a combination of the two experiments can be used to eliminate errors due to
friction.
Large-deformation and failure measurements must be carried out over a wide range of
strain rates (including very fast strain rates, where the experiment time is less than 1 s). If
the instrument is calibrated, and extensometers are
firmly, e.g. again using
'
superglue
'
fitted, it is easy to convert force and
amount of deformation into stress and strain. In this way the initial linear region can be
seen, and then the sample may either strain
'
harden
'
or
'
soften
'
(show upward or
downward curvature) before a clear failure point is seen.
A number of approaches can then be employed, but one which we have found useful,
although it has so far been employed sparingly in this area, is to construct the so-called
'
, originally suggested in the 1960s. By measuring the stress and strain
at failure (in tension) for a range of gels, each measured as a series of replicates and over a
wide range of extensional strain rates (say ~10
−
5
failure envelope
'
10
−
1
s
−
1
), and plotting failure stress
versus failure strain at various deformation rates, a graph
−
-
the failure envelope (Smith,
1963
)
can be constructed.
Under certain circumstances the compression of cylindrical gel samples, in practice by
far the simplest geometry and one still widely employed in industry, can still provide
useful information. For example, the work by Nakamura and co-workers (Nakamura
et al.,
2001
) has used this approach to compress samples of gellan gel (
Chapter 5
)ina
range of compression rates covering more than
-
five orders of magnitude. At the slowest
rates, a compressive de-swelling takes place; in other words, solvent is squeezed out of
the sample, but this can be recovered perfectly reversibly (and as expected) by allowing
the gel to re-swell in excess solvent. At higher compression rates, the gel fractures
(ruptures) instead. Unfortunately, analysis in terms of the more fundamental stress and
strain parameters is limited.
2.5.3
Particle tracking microrheology
Conventional rheological techniques as described above are widely used, but they do
have some limitations. In particular it is dif
cult to measure extremely tenuous gel
networks at the very small deformations needed to ensure that the reacting system is
within the linear viscoelastic limit. For this reason other
techniques
have a major potential advantage, and options employed over the last decade or so fall
under the general heading of particle tracking microrheology (PTM).
There are a considerable number of techniques in operation but, so far as we are aware,
no commercial equipment is available. The basic principle goes back many years, and
simple variations were apparently in use in the 1920s. Essentially a set of small micron-
size probes are placed in a (pre-gelled) solution and their position and velocity under
Brownian motion are followed, for example by laser scattering techniques. The exper-
imentally relevant measure is that of the set of (one-dimensional) mean square displace-
ments of the particles,
'
non-perturbing
'
x
2
x
2
. If the embedding
fluid is Newtonian, then
will be linear
〈
〉
〈
〉
with time t, following classical diffusion, and can be written
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