Chemistry Reference
In-Depth Information
it is probably most efficient to develop custom software to automatise
everything. Such a software also allows nearly real-time data analysis
and visualisation, which is crucial for industrial applications. Usually,
development environments such as MATLAB (Choi
et al.
, 2005) or
LabVIEW are used for implementation as they simplify the access to
the data acquisition hardware and also provide high-level function, for
example for non-linear fitting procedures.
3.6
PIPE FLOW AND FLUID MODELS
As mentioned in the introduction, the UVP-based in-line rheometry
makes use of the information contained in the shape of the flow velocity
profile. Frequently, the pressure drop over a straight pipe section is mea-
sured in parallel to the velocity profile. This allows the direct derivation
of the shear stress
τ
along the radius
r
, which is given by:
τ
=
Pr
2
L
(3.9)
where
P
is the pressure drop measured over a distance
L
along the
axial direction of the pipe (Fig. 3.1).
3.6.1
Gradient method or point-wise rheological
characterisation
The shear rate ˙
γ
along the pipe radius is given by:
d
v
d
r
γ
=−
˙
(3.10)
where
v
is the flow velocity along the radius
r
. Thus, using the measured
pressure drop and velocity profile, it is possible to derive directly the
local viscosity using Equations 3.9 and 3.10:
τ
(
r
)
η
=
(
r
)
(3.11)
γ
˙
(
r
)
In the articles from the University Erlangen-N urnberg (M uller
et al.
,
1997), this is described as 'gradient method', while the same principle
is described as 'point-wise rheological characterisation' in the articles
from the UC Davis (Arola
et al.
, 1999; Dogan
et al.
, 2005b), where the
measured flow profile was first fitted with a fourth-order polynomial
whose first derivative was then used to determine the shear rates.
