(153b) Characterization of Micromixing in a Rotor-Stator Spinning Disc Reactor: Effects of Gap Distance

In the chemical industry many processes involve complex
reaction systems where fast reactions take place, deriving in a range of
products while in fact only one is the desired one. In the past, in order to
achieve high selectivity and yield towards the main product, a common approach has
been to slow down the reactions by diluting the feeding streams, usually with
solvents. As a consequence, large reactors are needed to meet the production
requirements, and the removal of the solvents derive in high energy costs.

More recently, novel equipment has been developed in the
framework of Process Intensification (PI), aiming to enable production
conditions that were not possible with traditional equipment by the enhancement
of mass and heat transfer rates. With these novel reactors, high yields can be
obtained without the need to dilute the reaction systems.

In those high concentrated systems with higher reaction
rates, the selectivity is then determined by the mixing efficiency, especially
in systems where competitive consecutive or parallel competitive reactions take
place. More specifically, for very fast competitive reactions the micromixing
time -which is the homogenization of the system at the molecular scale-
determines the product distribution. The micromixing time has been extensively
investigated and well correlated to the turbulence intensity, mainly in stirred
vessels where homogenous and isotropic turbulence is observed.

For novel reactors such as the rotor-stator spinning disc
reactor, high shear forces applied to very small reaction volumes lead to a
very high turbulence intensity. These are in the range of 4 to 6 orders of
magnitude higher than those achieved in stirred vessels. In other words, very
high micromixing efficiency is expected[1].

In literature, there are models that can describe the
relationship between micromixing time and energy dissipation rate. The
micromixing time has been theoretically and experimentally determined to be
proportional to the Kolmogorov microscale:

Where ν is the kinematic viscosity of the fluid, ε
is the (local) energy dissipation rate. One of the most consistent models based
on turbulence theory is the Engulfment model[2].
In this model the term C takes a value of 17.23, based on a derivation from the
most hydrodynamic eddy of the turbulent field engulfing liquids from the
surroundings and allowing a small reaction zone to grow and react. Similarly,
other models like the incorporation model[3],
uses this term C as a correlation to obtain a micromixing time that is
proportional to the incorporation of liquids from the surroundings of the
reaction zone.

Furthermore, some test reaction systems have been developed,
in order to determine the micromixing times[4][3].
Assuming enough knowledge of the kinetics of the system, the fundamental basis
of these test reactions is that by performing competitive reactions, one can
analyze the product distribution and relate it to a micromixing time, using one
of the available models.

In the rotor-stator spinning disc reactors, the shear rate
and therefore the energy dissipation rate is known to have a proportionality to
the radius of the disc[5][6]:

The previous relationship allows for a good estimation of
the local energy dissipation rate by performing a momentum balance.

Naturally, by reducing the gap distance between the rotor
and the stator, the reactor’s volume will also decrease. This suggests that the
energy transferred from the disc into the liquid will be locally higher, and
also a function of the gap clearance. In the turbulent regime with merged
boundary layers, the shear rate –and energy dissipation rate– is a function of
the gap distance [5][6]:

Experimental results in a rotor-stator spinning disc reactor
at various gap distances show, however, that there is not significant effect observed
when modifying this parameter. In the first graph it can be observed that the
estimated local energy dissipation rate obtained from the momentum balance is
underestimated for bigger gap distances. On the other hand, on the second graph
the results indicate that the main parameter to define the micromixing time is
the rotational speeds.

The results suggest that the average local energy
dissipation rate estimated from the correlations from literature [6]
give a good approximation for the macromixing effects (bubble formation[5],
convective heat transfer[7],
mass transfer [8])
in the enclosed space between a rotating disc and a wall . However, for the
non-homogeneous, anisotropic turbulent field created by the high shear forces
in such a small volume, the local energy dissipation rate requires a
correlation to the tangential velocity. This is a topic of ongoing research.

Furthermore, a comparison between two test reaction systems
is presented, adopting a new kinetic model and addressing previous concerns
about the use of the Villermaux-Dushman system (unpublished work). With this
new kinetic model, lower micromixing times are obtained than those previously
reported using the Villermaux-Dushman method when compared to the
Diazo-coupling of naphthols [9].
This is however not surprising, since the iodide-iodate reaction in the
Villermaux-Dushman is much faster (kinetic coefficient in the order of
magnitude 8) than the diazo coupling of 2-naphthol (kinetic constant in the
order of magnitude 5). The iodide-iodate reaction occurs in a more localized
zone with higher turbulent intensity.

[1]        A. N. Manzano Martínez, K. M. P. Van Eeten, J. C. Schouten,
and J. Van Der Schaaf, “Micromixing in a Rotor-Stator Spinning Disc Reactor,” Ind.
Eng. Chem. Res., vol. 56, no. 45, pp. 13454–13460, Nov. 2017.

[2]        J. Baldyga and J. R. Bourne,
“Simplification of micromixing calculations. I. Derivation and application of
new model,” Chem. Eng. J., vol. 42, no. 2, pp. 83–92, Nov. 1989.

[3]        M.-C. Fournier, L. Falk, and J.
Villermaux, “A new parallel competing reaction system for assessing micromixing
efficiency—Determination of micromixing time by a simple mixing model,” Chem.
Eng. Sci., vol. 51, no. 23, pp. 5187–5192, Dec. 1996.

[4]        J. R. Bourne, O. M. Kut, and J. Lenzner,
“An improved reaction system to investigate micromixing in high-intensity
mixers,” Ind. Eng. Chem. Res., vol. 31, no. 3, pp. 949–958, Mar. 1992.

[5]        M. M. de Beer, J. T. F. Keurentjes, J.
C. Schouten, and J. van der Schaaf, “Bubble formation in co-fed gas–liquid
flows in a rotor-stator spinning disc reactor,” Int. J. Multiph. Flow,
vol. 83, pp. 142–152, Jul. 2016.

[6]        M. Djaoui, A. Dyment, and R. Debuchy,
“Heat transfer in a rotor-stator system with a radial inflow,” Eur. J. Mech.
B/Fluids, vol. 20, no. 3, pp.
371–398, 2001.

[7]        M. M. de Beer, J. T. F.
Keurentjes, J. C. Schouten, and J. van der Schaaf, “Convective condensation in
a stator-rotor-stator spinning disc reactor,” AIChE J., vol. 62, no. 10,
pp. 3784–3796, Oct. 2016.

[8]        M. Meeuwse, J. van der
Schaaf, B. F. M. Kuster, and J. C. Schouten, “Gas–liquid mass transfer in a
rotor–stator spinning disc reactor,” Chem. Eng. Sci., vol. 65, no. 1,
pp. 466–471, Jan. 2010.

[9]        P. Guichardon, L. Falk, and M. Andrieu,
“Experimental Comparison of the Iodide-Iodate and the Diazo Coupling
Micromixing Test Reactions in Stirred Reactors,” Chem. Eng. Res. Des.,
vol. 79, no. 8, pp. 906–914, Nov. 2001.