Investigations of mass transfer with chemical reactions in two-phase liquid–liquid systems
Introduction
The inability to mix reagents rapidly retards a single fast chemical reaction, which may result in a larger vessel or longer mean residence time to achieve a particular conversion compared to well mixed reagents. Similarly in complex reactions the conversion rates will also be reduced by poor mixing when the reaction rate is fast relative to observed mixing rates. Even more important are the reduced yields and the distribution of the reaction products (Bałdyga and Bourne, 1999). In this work we are interested in rotor–stator mixers that belong to the group of high-shear devices which are expected to be more energy efficient because of the focused delivery of energy. Consequently they are used in many industries including chemical, pharmaceutical, biochemical, agricultural, cosmetic, health care and food processing for homogenization, dispersion, emulsification, grinding, dissolving, performing chemical reactions with high selectivity, cell disruption and shear coagulation. High stresses and large values of deformation rate are generated in the rotor–stator mixers because the rotor is situated in close proximity to the stator and high rotor speeds are used. This requires a very high agitation power and hence, development of methods that can predict agitation power and efficiency of mixing is of the highest importance. In this context the opinion presented by Atiemo-Obeng and Calabrese (2004) is often cited, namely that “the current understanding of rotor–stator devices has almost no fundamental basis”, which has obvious consequences for design methodologies. However, considerable work has been done since 2004 on power draw during agitation (Bałdyga et al., 2007, Kowalski et al., 2011, Jasińska et al., 2012). In the present work a method that can be used to characterize mixing efficiency in a two-phase liquid–liquid system is proposed. The method is based on application of complex test reactions and follows the methodology that is traditionally used to study mixing in homogeneous systems (Bałdyga and Bourne, 1999). In this method the effects of process conditions on the product distribution from complex reactions are investigated, and the product distribution is afterwards linked to mixing energy efficiency using appropriate models. Using this method one can compare the energetic efficiency of mixing in systems of different geometry (Malecha et al., 2009). The method is based on the observation (Ottino, 1981) that the process of mixing between elongated but not completely mixed slabs can be represented by the rate of creation of the intermaterial area per unit volume, av [m−1], and is expressed by:where [s−1] represents the deformation tensor that is defined using the velocity gradient, grad(v).
Eq. (1) depicts the fact that orientation of the interface between different materials with respect to the principle axes of deformation determines effectiveness of mixing. Namely, not all the energy is dissipated due to flow and resulting fluid deformation increases intermaterial area; their effect can be opposite as well.
Using this concept one can define efficiency of mixing bywhere ɛT [m2 s−3] represents the total rate of energy dissipation per unit mass (Ottino, 1981, Rożeń, 2008). The procedure includes modelling of the effects of mixing on the course of the test chemical reactions using the E-model of micromixing (Bałdyga and Bourne, 1999). When micromixing is controlled by the viscous-convective engulfment process, then the concentration history can be calculated from the engulfment equationswith the engulfment parameter, E = 0.058(ɛ/ν)1/2, that depends on the rate of energy dissipation, ɛ. We use then the rate of energy dissipation, ɛ, as a reference value, characterizing the pure effect of elongation of structures present in eddies of the length scale equal roughly to 12λK (Bałdyga and Bourne, 1999) in isotropic, homogeneous turbulence. When as a system of test reactions comprising of a simultaneous diazo-coupling between 1- and 2-naphtols and diazotized sulphanilic acid is used, then there are two measures of product distribution, one concentrating on the yield of the secondary product S (a bisazo dye) and the other on the yield of the competitive product Q (a single monoazo dye). XQ is the fraction of the diazotized sulphanilic acid converted into Q and similarly XS presents the fraction of the diazotized sulphanilic acid converted into S. Effects of energy dissipation on XS and XQ are presented in Fig. 1, left; clearly in this case one should use XQ.
Comparing now the theoretical rate of energy dissipation, ɛ, necessary to obtain the same product distribution, XQ, as observed in considered experiment characterized by the rate of energy dissipation equal to ɛT, one can express the average efficiency of mixing, , by
The overbar in Eq. (6) denotes the value averaged over the residence time t in the mixer and means this fraction of the real rate of strain that is used directly to increase the intermaterial area. The rate of strain is expressed here using a root square of the second invariant of the deformation tensor.
In the case of the rotor–stator system the rate of energy dissipation depends on both the rotor speed N and the flow rate Q, so we express the observed value of the rate of energy dissipation as ɛT = ɛN,Q (Jasińska et al., 2012). Fig. 1 explains the procedure applied to identify efficiency of mixing. Applying this procedure to experimental data of Jasińska et al. (2012) one obtains results shown in Fig. 1, down. It shows that the efficiency of mixing in the rotor–stator for homogeneous system, where micromixing controls the course of chemical reactions, is between 6% and 35%, and decreases with increasing rotor speed. Such a decrease results from the fact that for smaller rotor speeds the reaction zone is localized close to the screen in the region of high dissipation rate, whereas for higher rotor speeds the reaction zone shrinks and is localized closer to the feeding point, where the rate of energy dissipation is relatively smaller. Notice that the fluid velocity is proportional to the rotor speed, N, whereas the rate of mixing is proportional to N3/2, so the mixing length which is then proportional to N−1/2 decreases with N. This illustrates how useful are reacting tracers to interpret mixing processes.
The aim of present study is to check the possibility of application of reactive tracers to the two-phase liquid–liquid system.
Section snippets
Theoretical background
When choosing the test reactions to study mass transfer in the liquid–liquid two-phase systems, one should have at least one reaction that is fast relative to mass transfer, so that the time constant of this reaction and mass transfer are either of comparable magnitude or the time constant for mixing is larger.
To study the effects of process conditions on reaction selectivity in the two-phase liquid–liquid system one can use the system of parallel second order reactions as follows.
Materials and methods
The parallel test reactions of the type presented in Eq. (7) were applied to study mass transfer in a two-phase liquid–liquid system. In experiments carried out in the batch reactor the continuous phase was an aqueous solution of sodium hydroxide (A) of initial concentration 0.005 mol dm−3 and the dispersed phase was a solution of benzoic acid (B) and ethyl chloroacetate (C) in toluene, both of initial concentration equal to 0.5 mol dm−3. The volume fraction of the organic phase was equal to 0.01.
Presentation and qualitative interpretation of experimental results
Fig. 5, Fig. 6 show the effects of agitation on pH and the product distribution for agitation with the 6-blade paddle. Effects of the rotor speed on pH and the product distribution, XS, for rotor–stator mixers equipped with both stators presented in Fig. 7, Fig. 8, Fig. 9, Fig. 10 show that for the GPDH the product distribution takes smaller values and the decrease of pH is faster than for SES, so the mass transfer is faster in the case of the GPDH, at least at not too high values of the rotor
Conclusions
The main message of this paper is that the course of parallel competitive reactions between sodium hydroxide present in aqueous solution, and either benzoic acid or ethyl chloroacetate present initially in the organic phase (toluene), is sensitive to agitation. Resulting product distribution, XS, can be used for direct comparison of effects of agitation in different systems as a segregation index for characterizing mass transfer in two-phase liquid–liquid systems. Results of investigations of
Acknowledgement
The authors wish to thank Mrs. Elizabeth Davenport, School of Chemical Engineering and Analytical Science, The University of Manchester, for her generous help in the GC–MS analysis carried out in this work.
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