Biomedical Engineering Reference
In-Depth Information
3
2
h
ˆ
o
G
eZ
(17)
sample
4
3
a
and
ˆ
sample
ˆ
Re
sampl
Z
are the imaginary and real part, respectively, of the sample
complex mechanical impedance
ˆ
sampl
Z
. It is important to note that for the calculation of the
storage modulus
G'
by Equation (16) is required to know the mass of the system, which
consist of an effective mass that includes the mass of the sample and the squeezing force
imposed to achieve good contact between the oscillating plate and the sample. If Equation
(12) is rewritten in terms of those masses we can obtain an equation for the measured
complex mechanical impedance:
Im Z
ˆ
ZR i
(
m
m
S
/
)
(18)
meas
sample
plate
effective
sample
ˆ
instrument
The inertia produced by the plate instrument can be easily estimated as
Z i
.
However, to estimate the inertia produced by the effective mass
m
effective
some additional
calculations are required. If the imaginary part of the sample impedance is divided by the
frequency, the following equation is obtained:
plate
ˆ
Im(
Z
)
sample
2
(
m
S
/
)
(19)
effective
sample
2
The term
S
/
in Equation (19) approaches to zero as the frequency is very high,
sample
ˆ
which results in
Im(
Z
) /
m
. Results of this calculation show that the parameter
sample
effective
ˆ
sampl
Z
reaches an asymptotic value, which is independent of the squeezing force
applied to the sample,
S
equals to
Im(
) /
m . That value can then be used to calculate the
storage modulus by Equation (16). Results for a xanthan gum suspension of concentration
2%, and whose mobility versus frequency data is shown in Figure 10, are shown in Figure 11
in terms of the viscoelastic storage and loss moduli defined by Equations (16) and (17). As
shown in the figure the data compares well with those obtained with a conventional
rheometer at comparable frequencies. It must be also noted that the range of frequencies of
the OSF method is significantly higher than those applied by conventional rheological
methods where inertia may play an important role.
effective
2.2.2 Semisolid materials
Physical properties of solid viscoelastic foods and other biological products are very
important in food production, storage, handling, and processing. The importance of the
knowledge of the physical properties of biomaterials is demonstrated in the case of fruits.
One of the most important quality parameter of fruits is its texture. Texture is the first
judgment a purchaser makes about the quality of a fruit, before sweetness, sourness, or
flavor. Since fruit texture is such an important attribute, one would expect the changes in
texture during maturation and cool-storage to be well understood, however this is not the
case. One of the main limitations to the study of fruit texture is the accurate and precise
measurement of texture as perceived by a consumer.
Traditionally, the texture of fruits is measured by a Magness Taylor pressure tester
(Magness and Taylor, 1925). This simple device measures the force required to insert a metal
