Chemistry Reference
In-Depth Information
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Gate #
Fig. 3.6
The velocity profile for Carbopol (grayscale, the frequency intensities;
∗
, the
envelope profile).
relation looks linear, so it can be fitted to the power law (Equation 3.13).
With a log transformation and the limitation of the shear rate range to
the one expected in the pipe flow (maximum 10/second), the values
resulting from the rheometer are
n
=
0.170
±
0.07 and
K
=
25.7
±
0.4
s
n
. The errors indicate the 95% confidence interval.
The measurement set-up consisted of a pipe with an inner diameter
of 25 mm, which was mounted at the exit of a kind of capillary rheome-
ter. The pressure drop was not measured, but the volume flow rate is
very well known. The ultrasound transducer was fixed in the pipe wall
(rightmost option; Fig. 3.3).
The measured Doppler shift frequency distribution for each gate (or
channel) is shown in Fig. 3.6 as surface plot. The darker the level of grey,
the higher the corresponding frequency intensity. In the same figure, the
envelope (maximum frequency) is indicated by symbols. The second
half of the profile shows some artefacts such as the beginning of a ghost
profile which is due to multiple reflections.
At the next step, the first half of the velocity profile obtained
f
rom
Equation 3.24 (Fig. 3.7) and the known volume flow rate
Q
(or
v
)are
used to determine
n
by fitting Equation 3.17. For the Carbopol profile,
the result is
n
Pa
·
=
0.177
±
0.07 which is quite close to the rheometer
result.
