Biomedical Engineering Reference
In-Depth Information
0.05
1% Xanthan Gum
2% Xanthan Gum
3% Xanthan Gum
0.04
0.03
0.02
0.01
0.00
0
20000
40000
Resonance Freq1% (rad/s)
Fig. 10. Mobility plots obtained with the OSF method for xanthan gum dispersions of
different concentrations
Although the mobility and the elastic and viscous components of a viscoelastic sample are
often useful as quality and processing parameters (Gonzalez et al., 2010), for modeling
purposes it is necessary to get quantitative and fundamental rheological information of a
sample in terms of elastic and viscous modulus. Phan-Thien (1980) demonstrated that for
viscoelastic materials subjected to squeezing flow under an oscillating plate, the squeezing
flow force can be calculated as:
4
3
a
*
(14)
F
cos(
t
)
u
cos(
t
)
o
o
3
2
h
o
*
where
a
is the radius of the top plate,
h
o
is the distance between plates and
is the
'
i
"
G
"
G
'
complex dynamic viscosity of the sample.
'
and
"
are the viscous and elastic
components of the sample, respectively. Application of FFT to Equation (15) yields:
4
3
a
ˆ
*
(15)
Z
sample
3
2
h
o
Expressions can be rearranged and using the definition of the complex viscosity
,
expressions for the viscoelastic moduli, i.e. the storage and loss modulus,
G'
and
G”
, can be
obtained as:
2
3
m
a
3
2
h
ˆ
effective
o
GImZ
(16)
sample
2
4
20
h
3
a
o
