INVESTIGATIONS OF MASS TRANSFER AND MICROMIXING EFFECTS IN TWO-PHASE LIQUID-LIQUID SYSTEMS WITH CHEMICAL REACTION

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1 14 th European Conference on Mixing Warszawa, September 20 INVESTIGATIONS OF MASS TRANSFER AND MICROMIXING EFFECTS IN TWO-PHASE LIQUID-LIQUID SYSTEMS WITH CHEMICAL REACTION M. Jasińska a, J. Bałdyga a, M. Cooke b, A. J. Kowalski c a Warsaw University of Technology, Faculty of Chemical and Process Engineering, ul Waryńskiego 1, Warsaw, Poland b School of Chemical Engineering and Analytical Science, The University of Manchester, PO Box, Manchester, M60 1QD, UK c Unilever Research & Development Port Sunlight, Quarry Road Eeast, Bebington, Wirral CH63 3JW, UK m.jasinska@ichip.pw.edu.pl Abstract. The product distribution expressed by reaction selectivity is a good measure of the competition between reaction, mixing and mass transfer. A new method based on experimental determination of the product distribution of a set of test, complex reactions has been introduced and applied to study mass transfer in liquid-liquid systems. The test reactions introduced in present work consist of two parallel reactions, one of them being instantaneous and the second fast relative to mixing and mass transfer. Two reagents are transferred from a dispersed, organic phase to the continuous aqueous phase, where they react with the third reagent that is present in the aqueous phase. Experiments were carried out in a batch system using the high-shear rotor-stator Silverson mixer for drop dispersion and intensification of mass transfer. Volume fraction of organic phase was equal to 1%vol. The product distribution of complex reactions was determined based on GC MS measurements. The same time variation of ph was recorded and the drop size distribution measured with the Malvern MasterSizer just after the process. Surfactant was added to stabilize dispersion and to avoid possible effects of droplets coalescence. Based on experimental results and theoretical analysis energetic efficiency of mass transfer was then identified and results were discussed. Keywords: chemical reaction, mass transfer, liquid-liquid dispersion, product distribution, selectivity. 1. 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 rates of complex reactions will also be retarded by not efficient mixing when they are fast relative to observed mixing rates. Even more important is another aspect of incomplete mixing, namely effect of mixing on yields and the distribution of the reaction products [1]. In this work we are interested in the rotor-stator mixers that belong to the group of high-shear devices. Due to focused delivery of energy to the regions that are active in the considered process they are expected to be very efficient energetically. That is why they are used in many technologies in the chemical, pharmaceutical, biochemical, agricultural, cosmetic, health care and food processing industries for homogenization, dispersion, emulsification, grinding, dissolving, performing chemical reactions with high selectivity, cell disruption and shear coagulation. High stresses are generated by applying high 175

2 rotor speeds, with the rotor that is situated in close proximity of a stator, which requires a very high agitation power. Hence, a good method to predict agitation power and efficiency of mixing is of highest importance. In this context opinion presented in Ref. [2], is often cited, namely that the current understanding of rotor-stator devices has almost no fundamental basis, which should have obvious consequences for design methodologies. However, much was done in this area after 2004 regarding power of agitation [3, 4, 5]. To find energetic efficiency of mixing in relation to homogeneous reactions one can use methodology presented in Ref. [6]. The method is based on the observation that the process of mixing between elongated, not completely mixed slabs can be represented by the rate of creation of the intermaterial area per unit volume, a v [m -1 ], and expressed by where D [s -1 ] represents the deformation tensor. 1 D = grad v + grad v 2 grad v. that is defined using the velocity gradient, ( ) 1 dav = eff ()( t D : D) (1) a dt v ( ) ( ) Eq.(1) depicts the fact that orientation of the intermaterial area with respect to the principle axes of deformation determines effectiveness of mixing. It characterizes the ratio of energy really applied to increase intermaterial area to the energy dissipated during the flow. Using this concept one can define efficiency of mixing by 1 dav εt eff () t = (3) av dt 3ν where ε T [m 2 s -3 ] represents the total rate of energy dissipation per unit mass. The procedure includes modeling of effects of mixing on the course of the test chemical reactions using the E-model of micromixing [1]. When micromixing is controlled by viscous-convective engulfment process, then the concentration history can be calculated from the engulfment equation: dc ( ) T i E ci ci Ri dt = + (4) dv = E V (5) dt with engulfment parameter 005 ε E =., that depends on the rate of energy dissipation, ε. ν Comparing now the theoretical rate of energy dissipation, ε, necessary to obtain the same product distribution, X Q, as observed in considered experiments, where the rate of energy dissipation is equal to ε T, one can express the average efficiency of mixing, eff, by ε eff = (6) εt The overbar in eq.(6) denotes the average values of efficiency during residence time t in the mixer. 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 ε T =ε N, Q. Figure 1 explains the procedure applied to identify efficiency of mixing. Applying this procedure to experimental data presented in ref. [5] one obtains results shown in Figure 1, right. 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 the rotor speed. 176 (2)

3 Figure 1. Schematic of the method applied to identify efficiency of mixing in homogeneous system for reactions carried out on the Silverson rotor-stator mixer: (left) theoretical dependence of the product distribution of diazocoupling reaction, X Q, on the rate of energy dissipation, ε; (middle) comparison of the observed rate of energy dissipation,, with the theoretical value, ε; (right) efficiency of mixing as a function of the rate of energy dissipation observed in experiments, ε N,Q. The aim of this study is to check the possibility of application of reactive tracers to the twophase liquid-liquid system. 2. THEORETICAL BACKGROUND When choosing test reactions one should consider the system of reactions with 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 effects of process conditions on reaction selectivity in the two-phase liquid-liquid system one can use the system of parallel second order reactions. k 1 k2 A B R, A C S + + (7) Notice that when the first reaction is very fast it can be controlled not by reaction kinetics but by the rate of mass transfer and then one has competition between the mass transfer process controlling the first reaction and chemical kinetics controlling the second one. Then extent of the second reaction can be used to characterise effectiveness of mixing. The time constant of the second reaction referring to the local feed concentration can be expressed by 1 τ r = () kc 3 C 0 Of course the following condition must be fulfilled, τ m τ r to ensure that the investigated system of reactions is able to characterise mixing correctly. This call for definition of mixing time for the two-phase system. From mass balance dcc Vd = AdkLΔ Cc (9) dt where V d and A d are the volume and surface of the drop and k L is the mass transfer coefficient. For a=a d /V d being the characteristic surface per unit volume of the dispersed phase, the time constant can be defined by 1 τ D = (10) ka L For spherical drops and using Batchelor [6] equation for the mass transfer coefficient and Kolmogorov [7] equation for the drop size one gets for k L a 177

13 2 16 0.6 D C D C ε 6 σ ka L = 2 + 0.69 ; dd = 0.23 (11) 0.4 0.

$0. 034 () 23 710 45 DC ε ρc Equations (11) and () are per unit volume of the dispersed phase of the volume fraction ϕ.$ Equations (11) and () show that to intensify the process for a given system one should decrease the time constant for mass transfer, τ M, by increasing the power input and related rate of energy

Equations (11) and () show that to intensify the process for a given system one should decrease the time constant for mass transfer, τ M, by increasing the power input and related rate of energy

$005 mol/dm 3 and the dispersed phase was a solution of benzoic acid (B) and ethyl chloroacetate (C) in toluene, both of concentration 0.5 mol/dm 3. Volume fraction of organic phase was 0.01.$

4 D C D C ε 6 σ ka L = ; dd = 0.23 (11) dd dd ν d d ε ρc For the Sherwood number much larger than 2 (Sh > 2) one has a simple relation between the rate of energy dissipation, ε, and the time constant for mass transfer σ ν τm = τd = () DC ε ρc Equations (11) and () are per unit volume of the dispersed phase of the volume fraction ϕ. They can be recalculated for the unit volume of the continuous phase by multiplying eq. (11) by ϕ ( 1 ϕ) and dividing eq.() by the same factor. Equations (11) and () show that to intensify the process for a given system one should decrease the time constant for mass transfer, τ M, by increasing the power input and related rate of energy dissipation, ε. 3. RESULTS AND DISCUSSION In this section the parallel test reactions of the type given by eq. (7) are applied to study efficiency of mass transfer in a two-phase liquid-liquid system. In experiments the continuous phase was an aqueous solution of NaOH (A) of concentration mol/dm 3 and the dispersed phase was a solution of benzoic acid (B) and ethyl chloroacetate (C) in toluene, both of concentration 0.5 mol/dm 3. Volume fraction of organic phase was During experiments the reaction between sodium hydroxide and either benzoic acid (instantaneous) or ethyl chloroacetate (fast) was localized in the aqueous phase. Experiments were carried out in the batch reactor of diameter cm, equipped either with the six-blade paddle (Figure 2a) or with the Silverson rotor-stator mixer (Figure 2b). In the case of the Silverson mixer a four blade rotor of diameter 31.2 mm and height.45 mm was used, and two stator geometries were investigated: standard emulsor screen (SES) (Figure 2c) and general purpose disintegrating head (GPDH) (Figure 2d). a) b) c) d) Figure 2. Experimental setup: a) 6 blade paddle, b) rotor-stator in batch system, c) standard emulsor screen (SES), d) general purpose disintegrating head(gpdh). NaOH solution (990 cm 3 ) was present in the vessel and the organic solution (10 cm 3 ) was added to start the process. The drop size was measured with the Malvern MasterSizer and ph recorded during experiments. Concentrations of ethanol and ethyl chloroacetate were measured after experiment using Gas Chromatography. The selectivity was defined as a fraction of moles of ester reacting with NaOH. XS = Δ NC NC0 (13) Figure 3 shows effects of agitation on ph and selectivity for agitation with the 6-blade paddle. 17

5 13 Exp_6, N = 200 rpm Exp_2, N = 244 rpm Exp_1, N = 305 rpm 0.6 Beaker (6 blade paddle) 15 min ph Exp_7, N =405 rpm Exp_3, N = 530 rpm Exp_4, N = 72 rpm Selectivity [ ] min time, t [s] Figure 3. Effect of agitation on ph and selectivity for agitation with the 6-blade paddle. Effects of rotor speed on ph and selectivity X S for rotor-stator mixers equipped with both stators are presented in Figures 4 and 5. ph standard emulsifier screen (SES) N = 2375 rpm N = 2375 rpm (shifted) N = 3065 rpm N = 4300 rpm N = 5100 rpm N = 5900 rpm time [s] Figure 4. Effect of rotor speed on variation of ph and selectivity. Silverson batch system. Vessel equipped with rotor-stator homogenizer with the standard emulsor screen (SES). selectivity N [rpm] standard emulsifier screen 15 min sample 30 min sample N [rpm] ph general purpose disintegrating head (GPDH) N = 2450 rpm N = 3150 rpm N = 400 rpm N = 5000 rpm N = 500 rpm selectivity time [s] N [rpm] Figure 5. Effect of rotor speed on variation of ph and selectivity. Silverson batch system. Vessel equipped with rotor-stator homogenizer with the general purpose disintegrating head (GPDH). Figures 4 and 5 show that for the GPDH the selectivity is smaller than for SES, so the mass transfer is faster in the case of GPDH, at least at not too high values of the rotor speed. On the other hand the drop dispersion process is more effective in the case of SES, where continuous decrease of the drop size down to 5µm is observed when the rotor speed is increased to 6000 rpm. In the case of GPDH the drop size decreases to about 14µm at about 4000 rpm and further decrease is not observed. This is shown in Figure 6. Both screens are used with the same rotor, which clearly shows that the standard emulsor screen (SES) should be chosen to make fine dispersions but it is less efficient in accelerating mass transfer. It is interesting that when the six-blade paddle is used the values of selectivity can be as small as 0.3, although the drops are as large as 40 µm to 0 µm. To explain observed effects an approach similar to the one applied for homogeneous reactions and presented in Figure 1 can be applied. To this end the model of mass transfer with chemical reaction is applied assuming that the neutralization reaction between benzoic acid (B) and NaOH (A) is instantaneous and using the rate constant for alkaline ethyl chloroacetate hydrolysis k 2 =23dm 3 /(mol s). The results of modeling can be presented as the calibration curves: X S versus k L a or X S versus ε. This is shown in Figure general purpose disintegrating head 15 min sample 30 min sample 179

6 2 24 general purpose disintegrating head standard emulsifier screen d 32 [μm] N[rpm] Figure 6. Effect of rotor speed on the drop size. Silverson batch system. Vessel equipped with rotorstator homogenizer. Comparison of results obtained with GPDH and SES. Figure 7. The smallest values of selectivity, X S, and related ε and k L a values: red 6-paddle impeller, green Silverson. Figure 7 shows that the Silverson rotor-stator batch mixers are not effective for mass transfer. Of course there is fast mass transfer within the mixer but most of the time the fluids are out of the mixer, in the bulk. There is no agitation in the bulk, so mass transfer is very slow. A gentle agitation with the six-blade paddle results in a more effective mass transfer (see higher effective rate of energy dissipation) than observed in the high-shear Silverson mixer. The focused supply of energy characterizing Silverson mixers is effective for such short term processes as drop breakage but not so effective for long term processes such as mass transfer. 4. REFERENCES [1] Bałdyga J., Bourne J.R., Turbulent Mixing and Chemical Reactions, Wiley, Chichester. [2] Atiemo-Obeng V. A., Calabrese R.V., Rotor-stator mixing devices, in: E. L. Paul, V. A. Atiemo-Obeng, S. M. Kresta (Eds.) Handbook of Industrial Mixing, Science and Practice, Wiley, Hoboken, New Jersey, [3] Bałdyga J., Kowalski A., Cooke M., Jasińska M., Investigations of micromixing in a rotor stator mixer, Chemical and Process Engineering, 2, [4] Kowalski A. J., Cooke M., Hall S., Expression for turbulent power draw of an in-line Silverson high shear mixer, Chemical Engineering Science, 66, [5] Jasińska M., Bałdyga J., Cooke M., Kowalski A., 20 Application of test reactions to study micromixing in the rotor-stator mixer, Applied Thermal Engineering, [6] Batchelor, G.K., 190. Mass transfer from a particle suspended in turbulent fluid, J. Fluid Mech., 9, [7] Kolmogorov A.N., Disintegration of drops in turbulent flows, Dokl. Akad. Nauk SSSR, 66,

APPLICATION OF TEST REACTIONS TO STUDY MICROMIXING AND MASS TRANSFER IN CHEMICAL APPARATUS

JERZY BAŁDYGA, MAGDALENA JASIŃSKA, JUSTYNA TRENDOWSKA, WIKTORIA TADEUSIAK *, MIKE COOKE **, ADAM KOWALSKI ***1 APPLICATION OF TEST REACTIONS TO STUDY MICROMIXING AND MASS TRANSFER IN CHEMICAL APPARATUS