(431d) An Improved Kinetic Model for Micromixing Characterization Using the Villermaux-Dushman Method

In the last few decades, Process Intensification (PI)
and the development of novel equipment have become key approaches for
engineers and scientist to tackle the challenges of the modern era. The
increasing effects of climate change require more effective measures to limit
emissions and develop more sustainable processes. Furthermore, industries have
the necessity of reducing waste generation but yet generate profits. However, for
new technology or new equipment to get into full scale implementation in
industry, sufficient knowledge needs to be acquired both in potential
applications as well as in economic feasibility.

In many industrial processes, reducing energy-intensive
separation steps during purification of final products could be achieved by
enhancing the selectivity towards the desired products, or by reducing
undesired by-products that in many cases are dangerous or harmful. This is
particularly difficult for processes that have fast reactions competing for a
limiting reagent, i.e., where micromixing plays an important role.

Micromixing is commonly defined as the homogenization of the
system at the smallest scale, where reaction occurs. The process has a
characteristic time, commonly called micromixing time, and it can define the
product distribution of fast competitive-consecutive or competitive-parallel
reactions. Typically, test reactions are used to measure qualitatively and
quantitatively the micromixing time in chemical reactors. One of the most
extensively employed test reaction systems is the Villermaux-Dushman system,
developed in the 1990’s [1]
and since then used to characterize both traditional and novel reactors[2][3].

The experimental method requires a small injection of acid,
which depending on the micromixing efficiency can favor one of the two possible
reactions: (1) neutralization of a buffer, or (2) iodide-iodate reaction.
However, the only way to quantitatively asses the micromixing time is having enough
information about the kinetics, and for some years there has been controversy
on whether the kinetic model for the iodide-iodate reaction is accurate enough
to quantify micromixing times[4].

In order to allow a quantification of the micromixing times
with this method, a new independent study was conducted, taking into account
the most recent findings on the topic and addressing the issues of the most
used kinetic model. Preliminary results indicate that the partial reaction
orders were in agreement with published models[5],
but the dependency of the kinetic constant on the ionic strength was
overestimated in previous studies[6].
The latter was determined using potassium sulfate to vary the ionic strength
together with the adoption of sulfuric acid as a proton source. These two
factors led to a “buffer-like” situation, slowing the reaction rate and hence
the apparent kinetic constant.

In this study perchloric acid, a strong monoprotic acid, was
used as a proton source. Furthermore, the inert salt used to adjust ionic
strengths was sodium perchlorate, to avoid undesired protonation of a weak base
such as potassium sulfate[7].
Fresh solutions of potassium iodide and potassium iodate were prepared for all
the experiments, varying concentrations to study the partial orders and
adjusting with sodium perchlorate to adjust to the desired ionic strengths. A
small batch reactor with integrated cooling to ensure a constant temperature of
20 °C was loaded with 50 ml of the solution. An injection of 1 ml of perchloric
acid at the desired concentration was added to start the reaction while
stirring the contents of the reactor with a magnetic stirrer. With in-line UV/Vis
spectroscopy the absorption at 353nm was used to determine the concentration of
triiodide using Beer-Lambert law.

Certainly the choice of the concentration set represented a
challenge during the experimental planning. First, the use of high concentrations
leads to a quasi-instantaneous reaction rate which cannot be accurately
determined. Second, the concentration of Potassium Iodide has to be
sufficiently high to push the equilibrium forward, and convert most of the
Iodine into triiodide. It was observed that failing to fulfill this condition
caused considerable evaporation of Iodine and a deviation of the observed
kinetic constant. Finally, increasing the ionic strength to 1M by adding sodium
perchlorate required also an increase of the acid concentration, because the
reaction rate was too slow to accurately measure it.

After the above considerations were taken into account, the
concentration sets were selected in such a way that reaction rates were fast
enough to avoid evaporation of Iodine over time (max. 300 seconds), but slow
enough to ensure the observation of a kinetic regime (min. 20 seconds). The
observed kinetic constant was fitted using the software Matlab for each
experiment. The following correlation between the kinetic constant and the
ionic strength was found:

The proposed empirical model (Eq 1) consists on an
“intrinsic” value at infinite dilution that decreases as the ionic strength
increases due to its impact on the activity coefficients of all the species.
The dependency of the activity coefficient on the ionic strength is expressed
in the form of a Debye-Hückel equation with one extra parameter, similar to
what Davies[8]
proposed. This model is in very good agreement, not only with previously
published kinetic data [5][8], 
but also with the most recent studies[10].

With this model, a more accurate estimation of the
micromixing times can be achieved, improving the quantitative characterization of
novel equipment such as rotating packed beds, spinning disc reactors,
rotor-stator mixers, micro-reactors, and more.

Furthermore, a new comparison of micromixing times obtained
with another test reaction (the diazocoupling of Naphthols) will be presented,
since previously there was a significant disagreement between the two methods[11].
Preliminary results of ongoing research show discrepancies that could be
attributed to the different characteristic reaction times more than to the
reliability of the systems.

References:

normal;text-autospace:none">[1]         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.

normal;text-autospace:none">[2]         M.
Assirelli, W. Bujalski, A. Eaglesham, and A. W. Nienow, “Study Of Micromixing
in a Stirred Tank Using a Rushton Turbine: Comparison of Feed Positions and
Other Mixing Devices,” Chem. Eng. Res. Des., vol. 80, no. 8, pp.
855–863, Nov. 2002.

normal;text-autospace:none">[3]         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.

normal;text-autospace:none">[4]         J. R.
Bourne, “Comments on the iodide/iodate method for characterising micromixing,” Chem.
Eng. J., vol. 140, no. 1–3, pp. 638–641, Jul. 2008.

normal;text-autospace:none">[5]         D. A.
Palmer and L. J. Lyons, “Kinetics of iodine hydrolysis in unbuffered
solutions.” 1989.

normal;text-autospace:none">[6]         P.
Guichardon, L. Falk, and J. Villermaux, “Characterisation of micromixing
efficiency by the iodide-iodate reaction system. Part II: Kinetic study,” Chem.
Eng. Sci., vol. 55, no. 19, pp. 4245–4253, Oct. 2000.

normal;text-autospace:none">[7]         A.
Kölbl, M. Kraut, and R. Dittmeyer, “Kinetic investigation of the Dushman
reaction at concentrations relevant to mixing studies in microstructured
cyclone type mixers,” Chem. Eng. Sci., vol. 101, pp. 454–460, Sep. 2013.

normal;text-autospace:none">[8]         C. W.
Davies, “Extent of dissociation of salts in water. Part VIII,” Trans.
Faraday Soc., vol. 28, pp. 2093–2098, 1938.

normal;text-autospace:none">[9]         S. M.
Schildcrout and F. A. Fortunato, “Spectrophotometric study of the rate of the
aqueous iodate-iodide reaction,” J. Phys. Chem., vol. 79, no. 1, pp.
31–34, Jan. 1975.

normal;text-autospace:none">[10]      G.
Schmitz, G. Bourceanu, and I. Ungureanu, “Effects of Ce(III) and Mn(II) on the
Dushman reaction and simulations of the Briggs–Rausher reaction,” React.
Kinet. Mech. Catal., vol. 123, no. 1, pp. 81–92, Feb. 2018.

normal;text-autospace:none">[11]      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.