CHAOTIC FLOW IN LAMINAR MIXING IN STIRRED VESSELS

Mixing in agitated tanks represents a fundamental part of
the chemical, petrochemical, pharmaceutical, food and
paper industries. This unit operation is commonly carried
out under steady flow conditions with the impeller
centered with respect to the vessel and rotating at constant
speed in one direction only. Mixing has been a popular
subject for the last years. Most studies have been focused
on power consumption, measurements of mixing times
and visualization of flow patterns. A number of techniques
have been developed for visualizing flow patterns in
stirred vessels. Mavros (2001) reviewed the use of very
sophisticated techniques for observing the flow behaviour
in stirred vessels including particles image velocimetry
(PIV), planar laser induced fluorescence (pLIF) and
thermal pulses, among others.
Mixing operations are usually carried out in some
applications at low to moderate Reynolds number, in
which the turbulent regime cannot be achieved. The
presence of important segregated regions and dead zone
generated with open impellers at low Reynolds number
has been extensively reported in the literature (Solomon et
al., 1981; Lamberto et al., 1996). Such pathologies persist
even if baffles and mixed flow impellers are used resulting
in very long mixing times, high energy consumption and
undesirable by-products due to poor reaction selectivity
can be generated. The most common way to vanish and
eliminate these regions consists of increasing the
rotational speed, however, this leads to an energy
consuming process, long mixing times, and in some cases
it may be detrimental to the final product especially when
mixing shear sensitive media.
It has been demonstrated that the flow structures generated
under steady flow conditions can be destroyed if the flow
is continuously perturbed if the impeller is lightly
displaced from tank centreline in the radial direction as
well as by using time-dependent revolutions. The works
reporting the use of spatial and temporal conditions
promoting chaotic flows in stirred vessels are reviewed in
this paper.
STEADY-STATE FLOW
Mixing operations are usually carried out at low to
moderate Reynolds number. The presence of important
segregated regions and dead zone generated with open
impellers at low Reynolds number has been extensively
reported in the literature (Solomon et al., 1981; Lamberto
et al., 1996). Those pathologies persist even if baffles and
mixed flow impellers are used resulting in very long
mixing times, high energy consumption and undesirable
by-products due to poor reaction selectivity can be
generated. The most common way to enhance mixing by
minimizing the effect of such non-homogeneities consists
of using wide impeller or increasing the rotational speed.
However, the latter option leads to high-energy levels and
in some cases it could be detrimental for materials
sensitive to shear.
Solomon et al (1981) reported for the first time the
observations of well-mixed regions around the impellers
surrounded by stagnant fluid, which are known as caverns
in the case of yield stress fluids. Considering a cavern as a
sphere with center on a Rushton turbine they proposed
empirical expressions for determining the geometrical
characteristics of such flow structures. The observations of
these flow structures were later confirmed by Alvarez et al
(2002) and Ascanio et al (2002).
UNSTEADY-STATE FLOW
The most common way to enhance mixing by minimizing
the effect of flow structures such caverns (well-mixed
regions) and isolated regions (static or quasi-static zones)
consists of using wide impellers or by increasing the
rotational speed. However, the latter option leads to highenergy
levels and in some cases it could be detrimental for
materials sensitive to shear. Therefore, other alternatives
based on the theory of chaos principles have been
developed and reported in the literature. They consist
basically on the use of spatial and temporal scenarios as
described below.

Eccentric impellers
Different alternatives based on pioneering studies on
chaotic laminar mixing have been reported in the
literature, in which it was demonstrated that
homogenization could be quickly achieved by using
eccentric cylinders rotating alternatively in both directions
during short times (Ottino et al 1988; Swanson and Ottino
1990; Muzzio et al 1991; Muzzio et al 1992). One of the
main reasons of using eccentric impellers is that they
provide the best mixing action where a vortex is not
required or not desirable.
Alvarez et al (2002) proposed the use of spatial conditions
based on the radial position of the impeller with respect to
the tank centreline. They showed that a minimal radial
displacement of the impeller can enhance the mixing
performance in terms of the mixing times. Similar results
were found by Ascanio et al (2002) by using different one
or two off-centered impellers in the stirred vessel.
Dynamic perturbations
Lamberto et al 1996 proposed the use of time-dependent
stirring speed to destroy the caverns generated under
steady mixing conditions. They demonstrated that the
mixing of Newtonian fluids could be clearly enhanced if
the fluid dynamics was continuously perturbed. This
method was shown to prevent the formation of segregated
regions close to the impeller, confirming the theoretical
results of Aref (1984). Using time-dependent rotation
directions changes conditions, Ascanio et al (2002)
demonstrated that segregated regions can be gradually
vanished and finally destroyed if the flow is continuously
perturbed.
It is clear from the above contributions based on the
fundamental concepts of chaos theory that nonconventional
mixing strategies appear to be promising to
enhance mixing in stirred tanks in laminar regime. During
the symposium a general overview of the works reporting
scenarios based spatial and temporal conditions will be
given for preventing the formation of coherent segregated
regions in the vicinity of the impeller resulting in energyefficient
processes.

Quantifying Mixing: The Exposure Dimension

Mixing, or Segregation, can be defined using three dimensions. The instantaneous state of segregation has two dimensions:
the scale of segregation, and the intensity of segregation. The intensity of segregation is reported as the CoV in a blending
application, while the scale of segregation is reported as the striation thickness distribution, the drop size distribution, as
examples. Previous work has shown that the two dimensions contain different and independent information. The CoV tells
us nothing about the scale of segregation, and the scale of segregation contains no information about the range of
concentrations observed.
The exposure dimension conbines the intensity and scale of segregation with a third characteristic of the system to give a rate
of reduction in segregation. Many examples of exposure equations are given in the literature. The most familiar is the mass
transfer rate, where the scale of segregation can be related to the interfacial area, the intensity of segregation to the local
concentration gradients, and the tendency of the system to reduce segregation to the mass transfer coefficient, or the
molecular diffusivity. In this case, the exposure dimension is an integral combination of the local area and intensity of
segregation, so while it is correlated to both the scale and the intensity of segregation, it is not a linear combination of the
average measures.
In this talk, the exposure dimension will be reviewed in the context of existing literature and models. The goal is to
determine the underlying mixing variables which consistently drive a reduction in segregation, and the role that these
variables play in achieving a range of process objectives

CAVERN FORMATION IN AGITATED PULP SUSPENSION STOCK CHESTS USING SIDE-ENTERING IMPELLERS

Pulp fibre suspensions display non-Newtonian rheology,
including a yield stress. Under certain mixer operating
conditions this creates caverns (regions of active mixing)
around the impellers with the cavern size affecting the
extent and quality of mixing attained. Due to the opacity
of pulp suspensions it is not possible to measure cavern
size with direct optical techniques, like photography.
Consequently two non-invasive techniques suitable for use
in opaque media were evaluated for determining the
cavern dimensions: electrical resistance tomography
(ERT) and ultrasonic Doppler velocimetry (UDV). The
agitation of several pulp suspensions in a 38 cm diameter
cylindrical vessel was studied using these methods over a
range of operating conditions. ERT is a non-invasive
technique that images differences in conductivity between
regions in the mixer using voltage measurements made at
the vessel periphery. Cavern measurement by ERT is very
rapid (data are collected within a few seconds) but it
suffers from poor spatial resolution (approximately 5 to
10% of the vessel diameter – from 1.9 to 3.8 cm in our
case). Two methods were evaluated for creating the
conductive environment imaged by ERT – the injection of
saline solution or the addition of small metallic tracer
particles to the region surrounding the impeller. UDV was
used to determine the cavern boundary by measuring the
locations at which suspension velocity fell to zero for
multiple linear paths through the vessel. While UDV
provided better spatial resolution of the cavern than ERT
(about 2 mm), multiple measurements (and consequently
significant time) were needed to build up the profile of the
cavern boundary.
Cavern size as a function of impeller rotation speed is
reported for a range of pulp suspension mixing conditions
(hardwood and softwood pulps, suspension mass
concentrations from 2 to 4%, two impeller offsets from the
wall, and two suspension height-to-chest diameter ratios)
in the 38-cm diameter cylindrical chest. A scaled version
of a commercially available axial flow impeller designed
for use in pulp suspension agitation (the Maxflo,
Chemineer Inc.) was used in the standard side-entering
configuration used for pulp stock chests. Measured cavern
diameters were compared against the axial force model
developed by Ammaullah et al. (1998) for predicting
cavern diameters in non-Newtonian fluids. The
discrepancy between the experimental data and model
predictions were fairly large, although they decreased with
increasing yield stress Reynolds number. The discrepancy
was attributed to the proximity of the impeller to the
vessel walls in the side-entering configuration studied. An
alternative correlation is presented for predicting the
cavern volume in pulp suspensions in this mixing
configuration based on the suspension yield stress

increasing yield stress Reynolds number. The discrepancy
was attributed to the proximity of the impeller to the
vessel walls in the side-entering configuration studied. An
alternative correlation is presented for predicting the
cavern volume in pulp suspensions in this mixing
configuration based on the suspension yield stress

Session

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