(132b) Macro-Mixing of the Dispersed Phase in An Immiscible Liquid-Liquid Stirred Reactor

Macro-mixing of the dispersed phase in an
immiscible liquid-liquid stirred reactor

Dang Cheng, Xin Feng, Jingcai Cheng, Chao Yang^*

Institute of Process Engineering, Chinese Academy of Sciences,

Beijing 100190, China

Abstract

Liquid-liquid dispersions in
mechanically agitated vessels are frequently encountered in chemical industry. The
dispersed drops are continuously broken and coalesced, which make such
processes extremely difficult to be well controlled. Numerous investigations have
thus been devoted to the two-phase dispersed systems because of their practical
importance and complexity [1]. Although they were widely studied in scientific and
engineering circles, there is still little information regarding the mixing in
either or both phases in stirred liquid-liquid dispersions. The knowledge of
macro-mixing, which is usually globally characterized by mixing time (also
termed as blend time), is essential when the mixing rate is comparable with or
slower than the chemical reaction rate. Under these circumstances, the liquid-liquid
mixing efficiency is found to have a profound impact on the overall performance,
e.g., production costs and product selectivities.

Mixing is a very complex
process in liquid-liquid dispersions, which can occur either in the continuous
phase or in the dispersed phase or in both phases. Recently,
Zhao et al. [2] investigated the macro-mixing of the
continuous phase in an immiscible liquid-liquid stirred reactor using the
conductivity technique, in which the tap water was taken as the continuous
phase and several oil phases were used as the dispersed phases, and their study
revealed the non-linear effect of the dispersed phase holdup on the continuous
phase mixing time. The macro-mixing process in the continuous phase of a multiphase
system is achieved by convective (bulk) and turbulent (eddy) motions. However, the problem of mixing amongst the
dispersed phase (drops), i.e., the dispersed phase mixing, is of special interest for
such practical applications as suspension and emulsion polymerization,
i.e., reactions occurring in the dispersed phase, in which the dispersed phase mixing
may greatly influence the productivity and selectivity. Experimental
measurements and theoretical studies have shown that the dispersed phase mixing
had a significant influence on the average reaction rates and product selectivities
in non-first order or mass transfer controlled reactions occurred in the
dispersed phase [3,4].

The dispersed
phase mixing
is fulfilled by means of intense drop interactions (dispersion, breakup and coalescence),
which control the species concentration distribution among drop population. The
drops are naturally completely segregated in liquid-liquid dispersions, if
there is no dispersed phase mixing or there is no segregation (no concentration
difference among drops) at an infinite dispersed phase mixing rate (or
interaction rate) between the dispersed drops. Rietema [5] stated that the two
extreme cases did not really exist in practical industrial processes and usually
there was a finite interaction rate or partial segregation. Thus in many practical
reactors the dispersed phase cannot be considered to be either totally unmixed
or perfectly mixed. On analyzing the problem, there arises the question to what
an extent the drop concentrations can be mixed and how long it usually takes
for an added nontransferring tracer to be mixed to an expected extent. However,
it is particularly noted that quantitative measurement of the macro-mixing
process in the dispersed phase is still an unresolved problem, despite of its practical
importance.

In our previous works [2,6,7],
the macro-mixing and two-phase flow in the continuous phase in immiscible
liquid-liquid stirred tanks have been studied by experiment and numerical
simulation. In this work we focus on experimental measurement of the dispersed
phase mixing time, which is defined as the time required to achieve certain degree of macroscale homogeneity
of an inert nontransferring tracer injected into the liquid-liquid
dispersion, using
the planar laser induced fluorescence (PLIF) method. The PLIF technique requires that the
dispersed phase invisible in the continuous phase by matching the refractive
indices of the immiscible liquid-liquid pair in order to obtain clear images, particularly
for the measurement at high holdups of the dispersed phase. The ideal liquid-liquid
pair is selected for the PLIF experiment: NaI (in an aqueous solution of 0.02 M Na₂S₂O₃) as the dispersed aqueous phase and silicone oil as the continuous phase.

Experiments are
carried out in a batch manner in a transparent Plexiglas stirred reactor
(cylindrical, flat-bottom). The diameter (T) of the stirred reactor is 120 mm and the total height is 216 mm. Four vertical baffles with width (B) of 12 mm are equipped equally-spaced at the wall. The liquid height for all experiments is set at H=T. Different types of stirrers are used, namely, Rushton
disk turbine (RDT), half circle blade disk turbine (HCDT), 45° pitched blade
turbine downflow (PBTD) and 45° pitched blade turbine upflow (PBTU). The four
impellers have the same diameter (D=T/2). An outer transparent Plexiglas
square tank (160 mm°Á160 mm°Á216 mm) is installed around the stirred reactor to minimize the optical reflections and distortions at the cylindrical wall.

A Nd:YAG laser (Beamtech Optronics Co., Ltd., China) is used as
the illumination source. The laser emits a beam of 532 nm wavelength. The
fluorescence emitted by the tracer is recorded by the digital CCD camera (Imperx,
Inc., USA, 12 bits) placed perpendicularly to the plane of the laser sheet. The
size of the recorded pictures is 2048°Á2048 pixels² which corresponds
to a measurement field of 15 mm°Á15 mm. A 105 mm objective (Micro-Nikkor 105 mm
f/2.8G) and a sharp-cut glass filter (560 nm) are used on the camera to
eliminate the overlapping effect of illumination and emission, and also to
ensure that the reflected or scattered laser light does not interfere with the
fluorescence measurement during PLIF image acquisition. Rhodamine B (A.R.) is
used as the tracer, which is a nontransferring dye indissolvable in silicon oil.
Before starting the experiments, it is necessary to determine the linear
response range between light intensity and the concentration of Rhodamine B in
single-phase and two-phase systems for our specific laser, camera, and setup
geometry.

In our experiments, a very
small volume of the aqueous standard solution containing Rodamine B is injected quickly into the experimental system. The way of defining a degree
of macro-mixing is through the spatial variance of the concentration, which is
defined as

         
   (1)

where m_x
and n_z are the numbers of pixels at radial and axial
direction for the characterized zone, respectively, and i and j
are position indices of a pixel in this zone. This criterion is based on the
decay of the normalized concentration variance, where  is the average gray value
for the specified zone over 200 fully mixed images, and
 is the average gray value
for the specified zone over 200 images before tracer injection (t=0). It
can be seen from Figure 1 that a plot of the calculated variance is shown in a
semi-log scale.

Figure 1. Degree of mixing versus time (PBTU, C=T/2, N=410
rpm, ¦Á_d=10%)

The curve in
Figure 1 expresses the decay of the concentration fluctuations after injection
of the tracer. Theoretically, if the dispersed phase mixing rate is high enough,
the  value can vary
from zero for an unmixed state to -±for perfect mixedness. Whereas, it is
noted from Figure 1 that  cannot even reach
the 95% homogeneity (i.e. =-2.6), suggesting that the
tracer in the dispersed phase cannot be mixed to a perfectly mixed state. This
is a notable difference between the turbulent dispersed phase mixing and the
continuous phase or single liquid phase mixing. The mixing time is thus defined
as the time when , i.e., ,
which is a 90% approach to the perfectly mixed state. The t_m
obtained from this criterion is 31.8 min.

The variables studied are
tracer injection position, impeller type, impeller off-bottom clearance, agitation
speed, dispersed-phase holdup, viscosity of the continuous phase. An effective model for
predicting the dispersed phase mixing time is also developed in this work.

Keywords: dispersed phase mixing; mixing
time; liquid-liquid; stirred reactor

References

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