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Mixing on the molecular scale (micromixing)
MIXING
ON THE MOLECULAR
Teclmisch-chemisches
SCALE
(MICROMIXING)
J. R. BOURNE Laboratorium ETH, CH-8092 Zurich, Switzerland (Received 12 August 1982)
HLSTORICAL
PERSPECTIVES
concentration) of interest. Danckwerts [3] recognized that “large-scale segregation caused, for instance, by sedimentation or by dead space in a mixer is of great practical importance, but its study cannot conveniently be combined with that of the small-scale characteristics, or texture, which are the subject of the present discussion. The subject of large-scale segregation in continuous flow systems will be dealt with on another occasion”. This occasion was Ref. [l]. Even in the absence of large-scale variations, Danckwerts’ analysis focuses attention on the need to specify two parameters in order to characterise segregation. However, the scale and intensity of segregation defined by Danckwerts have not been widely employed, since they are usually difficult to determine. The value of these quantities is rather that they provide a conceptual framework within which, for example, an experimentalist can think about what his measurement of “goodness of mixing” means and an engineer can more effectively consider the performance data of a mixing machine or plan a mixing process. The significance of the scale and intensity of segregation in the context of chemical reactors will be discussed below. In contrast to this treatment of local texture, the classical residence time distribution paper [I] was concerned with the characterisation of the flow pattern in a continuously operated device and especially with backmixing. The large scale fluid dynamics are primarily convective and are not directly related to mixing on the molecular scale and the associated intensity of segregation. Questions of residence time distribution are therefore treated in a separate article. Although considerations of the local texture of finegrained mixtures apply for example to aerosols, emulsions, precipitates, pigments and many other non-reactive systems, they apply in particular on the molecular scale, i.e. to chemical reactions in inhomogeneous mixtures. (The prefix micro was used by Van Krevelen [4] in this context, whereas Danckwerts wrote of mixing on the molecular scale.) Danckwerts in two papers appearing in 1958 again set the course of much subsequent research. Already in 1953 the intensity of segregation at the molecular scale had been related to the observable rate of a second order reaction taking place between reagents, which were initially present in separate streams (31. Thus. in the limit, no reaction can occur when segregation is complete and the rate attains its maximum value when the mixture is chemically uniform. Any segregation present must therefore retard reaction. The 1958 paper
1950s The literature of the 1940s and the early 1950s reveals little research into mixing, but rather for example into distillation, liquid extraction and the then new technique of fluidisatioo. Mixing research consisted of applying the methods of engineering fluid mechanics to stirred tanks. The drag on an impeller was considered and the power number-Reynolds number curves of many industrially used stirrers were determined, notably by Rushton et al. The pumping capacity of an impeller, the total flow circulating in a tank and the role of batlIes in vortex suppression and turbulence generation were investigated. The year 1953 marked, however, a turning point. Danckwerts published not only his celebrated paper on residence time distribution [l], but also two papers addressing themselves to the quality of mixing [2] (what do we mean when we say that something is mixed?) srnd its quantitative difioition and determination [3] (how is goodness of mixing to be determined?). Many concepts and definitions, which have since become classical, were introduced. The review “Theory of Mixtures and Mixing” [Z] expressed our notion of the scale of scrutiny as follows: “Unless the reasons for making up a mixture are known, it is impossible to decide whether it is well or badly mixed. Any mixture, if scrutinized closely enough, will show regions of segregation-that is, the composition will vary from point to point. The size of the regions of segregation which can be tolerated will vary from one case to another. The term “scale of scrutiny” will be applied here to the minimum size of the regions of segregation in #he mixture which would cause it to be regarded as imperfectly mixed for a specified purpose. Defined in this imprecise way, the scale of scrutiny can only be expressed as an order of magnitude (length, volume or area), but the concept is a useful one.” The probably better known paper “The definition and measurement of some characteristics of mixtures” [3] considered the local texture of a non-uniform mixture. (The only important restriction is that this mixture shall be fine-grained, i.e. the scale of scrutiny shall encompass a large number of particles (ions, molecties etc.) of each component e.g. solutions and mixtures of gases. When fully randomized such a mixture will be essentially uniform in composition). Two quantities characterising finegrained mixtures were defined, the scale and intensity of segregation. Roughly speaking these express the extent and amount of variability of the local property (e.g. me
5
6
J. R.
“The effect of incomplete mixing on homogeneous reactions” [5] revealed that when a second order reaction is used as a chemical tracer to measure the intensity of segregation, the reaction should be slow enough that practically no reagent is consumed in the This restriction reactor. often produces contradiction, since slow reactions cause little segregation. The situation where a single feed stream, containing all necessary reagents, enters a reactor and mixes with its contents was also treated by Danckwerts [S]. This results in dilution of the fresh reagents and therefore in a retardation of reaction. That mixing can either accelerate or retard reaction, depending upon whether the reagents enter the reactor separately or pre-mixed respectively, was clearly recognized by Danckwerts [5], has however caused some confusion in the literature. Thus some writers use the terms species mixing and self mixing (age mixing) respectively to distinguish the two cases, although the same mechanism (mixing on the molecular scale) is operative in both. In 1958 Danckwerts also published “Measurement of molecular homogeneity in a mixture” [6] giving a method which has been developed and widely applied by Hiby et al. [7]. In essence Danckwerts showed how to use a diffusion controlled reaction (e.g. neutralisation) to determine the intensity of segregation. The limitations inherent in this approach are not experimental, but relate to the significance of the intensity of segregation. For example, suppose it has been measured and a different, slower reaction is to be carried out in the same apparatus under the same hydrodynamic conditions. The segregation will be lower, but there is no way of predicting it from the acid/base measurements. The difficulty is that the intensity of segregation depends upon the interaction between the diffusional flux and the reaction kinetics (see next Section). It is a characterising variable, unrelated to the underlying transport phenomena. By the end of the 1950s backmixing, species mixing, self-mixing, segregation etc. had been thought out by Danckwerts, perhaps in moments of “academic indolence” [S]. and had started to enter into the conciousness of many chemical engineers. To a large extent Danckwerts left the development of new theories of mixing and the treatment of more complex problems, e.g. precipitation, nucleation, combustion, selectivity in multiple reactions, to others. He pursued his other line of research, gas absorption especially when accompanied by chemical reaction [9]. And yet is it so other? The absorption of a gas by a liquid is not only formally analogous to the mixing of separate feed streams in a reactor. It relies on the same mass transfer mechanisms and the concentration gradients set up produce the same effects, namely a reduction in rate and possibly a modification of selectivity relative to the state of homogeneity on the molecular scale. PERSPECTIVES M MICROhiawG
The 1960s During this period several experimental studies sought to decide if the continuous stirred tank reactor operating with a single feed stream was best described as
BOURNE
homogeneous, fully segregated [S] or partially segregated. This was directly inspired by Ref. [5]. The results were, however, inconclusive. The stirrer speeds and feed positions used were so abnormal that the residence time distribution deviated from good mixing and the measured rise in conversion could seldom be attributed unequivocally to inhomogeneity at the molecular scale. In retrospect it seems that the reactions were too slow and the solvents insufficiently viscous to induce segregation. Duckwerts’ ideas about segregation in reactors [5] also set off attempts to model partial segregation, most effort being devoted to the single feed stream case. The topic of micromixing began to become divorced from reality for the following reasons: (a) most models lacked a physical (e.g. fluid mechanical) basis: (b) the model parameters were seldom known independently, but rather were fitted, and this established nothing and (c) the limits of conversion between homogeneous and completely segregated mixtures are widest for the continuous, well-mixed tank reactor and yet amount to at most 7% for a second order reaction. (Multiple reactions can exhibit somewhat wider limits, but were not intensively studied during the 1%0’s). Apart from polymerization, where particularly the termination step of addition reactions can be diffusion controlled (NorrishTromsdorf effect), the risk of solving a non-problem was great. The Proceedings of the international meetings on Chemical Reaction Engineering also reveal this. The 1970s and 1980s It now seems clear that: (a) inhomogeneity at the molecular scale develops if the half-life time which would be required by chemical reaction in a homogeneous solution is of the same order as or less than the half-life time for micromixing in the absence of reaction [lo, 121; (b) micromixing proceeds by molecular diffusion in small fluid elements which are being gradually strained [M-13]. The way in which these conclusions have been reached wiU now be outlined. Two miscible solutions, each containing one of the reagents A and B, are to be mixed in turbulent flow. Suppose that the B-rich solution is much more concentrated, so that less of it must be used to obtain a given stoichiometric ratio. Mixing consists initially of convective or flow-dominated processes, namely distribution and turbulent dispersion, whereby fresh, B-rich fluid elements are deformed until their scale of segregation is comparable to the Kolmogoroff velocity microscale. Mixing continues below this scale by molecular diffusion, which reduces the intensity of segregation, and also by laminar strain, which reduces the scale further and accelerates diffusion [lo, 121. Quantitative modelling consists of the unsteady state diffusion equation with a convective term for the simultaneous shrinkage of the fluid element. First estimates of the initial size and the rate of deformation can be obtained from the energy dissipation rate and the kinematic viscosity [l&12]. Use of diffusion-reaction equations to describe the course of a reaction during micromixing leads to the second Damkoehler number (or what elsewhere we have termed the mixing modulus [lCl]),
7
Mixing on the molecular scale (micromixing) which is proportional to the ratio of the diffusion time to the reaction time, i.e. its value indicates whether the reaction regime is slow (controlled by kinetics), fast (kinetics and ditfusion both important) or instantaneous (fully diffusion controlled). Fast reactions in a single phase, the inlluence of pore diffusion on reaction rates in porous catalysts (Thiele modulus) and the retardation of the rate of a gas/liquid reaction by diffusion through the liquid film (Hatta number [9] is proportional to the square root of the ratio of the diffusion and reaction times) are today all described by the same principles. APPLICATIONS
In turbulent aqueous solutions it is readily shown that only reactions having half-lives of less than around 0.1 s are likely to take place under conditions of partial segregation. Clearly a pre-mixed feed stream will not be used for such reactive materials and only the separate feed stream case is relevant. A fast single second order reaction will then be retarded by segregation, but the resultant loss of conversion can frequently be compensated by an increase in the reactor volume. Fast multiple reactions, whose product distribution depends upon mixing on the molecular scale, produce a different product spectrum when segregation occurs. This wastes raw materials and complicates the separation following the reactor. It cannot moreover be compensated by changing reactor volume. Thus the effect of segregation upon some multiple reactions is likely to be economically and ecologically more serious than when conducting a single reaction. 114. 151; (b) Examples include: (a) copolymerization autocatalytic reactions [16, 173; (c) competitive, consecutive reactions, where changes of selectivity caused by segregation of up to two orders of magnitude have been measured, e.g. single phase nitrations [18, 191, brominations [20,21] and iodinations [22,23] of aromatic compounds, as well as some diazo couplings [24-261. These substitutions exhibited the maximum yield of the intermediate in a reaction sequence in the slow reaction regime and a drastic loss of yield towards the instantaneous regime. In some examples even isomer distributions depended upon segregation [20,27]. Almost all the results obtained with these reactions are qualitatively consistent with the mechanism of mixing on the molecular scale outlined above. In those few cases where sticient information on reaction mechanism, kinetics, reactor configuration etc. was available, good quantitative agreement has also been obtained [IO-121. TWO-PEASE
REACTIONS AND MICBOMCUNG
Fast single phase reactions and two phase reactions have been described by diffusion-reaction equations as noted above. The purpose of this short section is to stress the similarity of the effect of mixing on product distribution in the two cases. Parallel reactions e.g. alkylation and competitive, two-phase [28,291 nitration of benzene and toluene [30.43]: the results for these two-phase systems are qualitatively the same as for homogeneous reactions (31). Competitive, consecutive reactions, e.g. chlorination of
hydrocarbons [32-341, of p-cresol[35-371 and of acetone [38] and sulphonation of benzene [39, 401: in all cases less intensive mixing, denoted by a fall in the liquid film mass transfer coefficient and thus an increase in the diffusion path length, caused a lower yield of intermediate. This trend is the same as that observed with fast, single phase reactions and was typically caused by the second reaction in the lilm becoming fast. A fine example of the applicability of diffusion-reaction theory to the chlorination of p-cresol has been given by Pangarkar and Sharma [37]. In the experimental part of this study all requisite physico-chemical quantities were determined independently (solubility and diiusivity of chlorine, rate constant of each of the two chlorination& and the liquid film mass transfer coefficient). Three different reaction regimes were predicted and also realized, whereby the selectivity for the monochloro-derivative varied over one order of magnitude. Provided sufficient physico-chemical data are known, product distributions from fast, homogeneous and heterogeneous reactions can now be predicted with suflicient accuracy for many purposes. THEFUTURE
Ten years ago few convincing examples of mixingcontrolled product distributions were knowu. Experimental and theoretical research has now established such phenomena. With the symptoms becoming clearer, it is likely that further examples will be recognized and further improvements in selectivity will be attained. A likely field for advances is polymerization [41]. Evidence of the large effect of viscosity on micromixing exists (25, 421, whereas macromixing in the turbulent regime is scarcely dependent upon viscosity. The new model of micromixing should be applied to predicting the effect of viscosity on polymerization, and attention paid to the possible simultaneous development of temperature segregation in viscous fluids. Many enzyme catalysed reactions are very rapid and bacteria and other micro-organisms are around one order of magnitude smaller than the Kolmogoroff eddies. The mechanism of micromixiug will therefore also be relevant for reaction and mass transfer [44] at such scales. Perhaps the dependence of yield in some fermentations upon agitation conditions will be explicable and quantitatively describable in terms of micromixing. With fast reactions the feed stream can start to react locally before it has been mixed on the molecular scale with the whole reactor contents and this can be detrimental to selectivity or even dangerous. Now that chemical tracers sensitive to micromixing are available, they can be used to improve the design and location of feed ports. “It is important to discover how much of the energy supplied to the mixer is essential and how much is dissipated fruitlessly” [2]. Since 1953 much has been learned about this matter in the fields of gas dispersion, heat transfer and partMe suspension in stirred tanks. The newly emerging mechanism of micromixing predicts: (a) a scale-up criterion of constant power per unit volume for the rate of mixii at the molecular scale; and (b) all mixing devices operated at the same power per
8
I. R. BOURNE
unit volume will generate the same rate of micromixing. Evidence on these two matters will accumulate and generate new guidelines about “absolute energetic efficiencies” [2] in the context of mixing on the molecular SC& REFERENCES
Danckwerts P. V., Chem. Engng Sci 1953 2 1. Danckwerts P. V., Researck 1953 6 355. Danckwerts P. V., Appl. Sci. Res. 1952/3 A3 279. van Krevelen D. W.. Ckem. Engag S’ci 1958 8 5. Danckwerts P. V., Ckem. Engng Sci. 1958 8 93. Danckwerts P. V., Ckem. Engng Sci 195718I 116. Hiby J. W., Ckem. Ing. Technik 1979 51704. Danckwerts P. V., Insights into Chemical Engineering. Pergamon Press, Oxford (1981). Danckwerts P. V., Gas-Liquid Reactions. McGraw-Hi& London (1970). Angst W., Boume J. R. and Sharma R. N., Chem. Engng Sci. 1982 31 585. Angst W.. Bourne J. R. and Sharma R. N., Chem Engng Sci. 1982 37 12.59. Bol~em 0. and Bourne .I. R., Cheat. Engng Sci. in press. Danckwerts P. V., Diflusion Processes (Edited by Sherwood J. N.), Vol. 2, p. 545. Gordon & Breach, London (1971). Szabo T. T. and Nauman E. B., A_I.Ch.E.J. 1969 15 575. Mecklenburgb J. C., Can. I. Chem. Engng 1970 48 279. Plasari E., David R. and Vihermaux J., Am. Ckem. Sot. Symp. Ser. 1978 65 125. Plasari E., David R. and Villermaux, J. Nouveau J. C/rim. 1977 149. Hanna S. B., Hunziker E., Saito T. and Zoltiier H., Helv. Ckim. Acta 1%9 52 1537. Nabholz F. and Rys P., Helv. Chim. Acta 1977 60 2937. Boume J. R., Rys P. and Suter K., Ckem. Engng Sci. 1977 32 711. Bourne J. R. and Kozicki F., Chem Engng Sci. 1977 32 1538. Paul E. L. and Treybal R. E., A.I.ChE.J. 1971 17 718. Zoulalian A. and Viiermaux J., Am. Ckem. Sot. Adean. Ckem. 1974 133 348.
[24] Boume J. R., Kozicki F. and Rys P., Cheat. Engag Sci 1981 36 1643. [ZS] Bourne J. R., Kozicki P., Moe&i U. and Rys P., C/rem. Engng Sci 1981 36 1655. 1261 Belevi H., Boume J. R. and Rys P., Helu. Ckim. Acta 1981 64 1618. [27] Boume J. R., Crivelli E. and Rys P., Helo. Chim. ACM 1977 60 2944. [28] Li K. W., Eckert R. E. and Albrlght L. F., Jnd. Eng. Ckem. Proc. Des. Dev. 1970 9 434. [29] Allan D. E. and Caulk R. H., Am. Chem. Sot. Nat. Meet. Petr. Sec. paper 11, March 1977. [30] Hanson C. and Ismail H. A. M., Chem. Engng Sci. 1977 32 775. [31] Bourne J. R. and Toor H. L., A.LCk.EJ. 1977 23 602. [32] van de Vusse J. G., Chem. Engng Sci. 1966 21 631. [33] Ramage M. P. and Eckert R. E., Ind. Engng Chem. Fundls 1979 18 216. [34] Kondelik P. and Pasek J., Coil. Czech. Ckem. Common 1981 46 1635. [35] Teramoto M., Nagayasu T., Matsui T., Hashimoto K. and Nagata S., J. Chem. Engng Japan 1969 2 186. i361 Teramoto M., Fujita S., Kataoka M., Hashhnoto K. and Nagata, S., .I. Ckem. Engng Japan 1970 3 79. 071 Pangarkar V. G. and Sharma M. M., Chem. Engng Sci. 1974 20 561 _____. [38] Paul E. L., Aiena J. R., N Nusim S. H. and Sklarz W. A., A.I.Ck.E. Ann Merting paper 18f, November 1981. [39] Beenackers A. C. M. and van Swaaij W. P. M. Ckem. Engng J. 1978 15 25, 39. 1401 +utckers A. C. M., Am. Chem. Sot. Symp. Ser. 1978 65 [41] Ottino J. M., Chem. Engng Sci. 1980 35 1377; Chella R. and Ottino I. hf., Proc. 7fh Ckem. React. Engng Symp., Boston October 1982. [421 Bourne J. R.. Schwarz G. and Shanna R. N.. Proc. 4th Euro. Conf. on Miring, p. 327. BHRA Fluid Engng, Cranheld 1982. [431 Schofield K.. Aromafic Nitration, Chap. 8 University Press. Cambridge 1980. i441 Batchelor G. K., J. Ruid Meek. 1980 98 609.
ON THE MOLECULAR
Teclmisch-chemisches
SCALE
(MICROMIXING)
J. R. BOURNE Laboratorium ETH, CH-8092 Zurich, Switzerland (Received 12 August 1982)
HLSTORICAL
PERSPECTIVES
concentration) of interest. Danckwerts [3] recognized that “large-scale segregation caused, for instance, by sedimentation or by dead space in a mixer is of great practical importance, but its study cannot conveniently be combined with that of the small-scale characteristics, or texture, which are the subject of the present discussion. The subject of large-scale segregation in continuous flow systems will be dealt with on another occasion”. This occasion was Ref. [l]. Even in the absence of large-scale variations, Danckwerts’ analysis focuses attention on the need to specify two parameters in order to characterise segregation. However, the scale and intensity of segregation defined by Danckwerts have not been widely employed, since they are usually difficult to determine. The value of these quantities is rather that they provide a conceptual framework within which, for example, an experimentalist can think about what his measurement of “goodness of mixing” means and an engineer can more effectively consider the performance data of a mixing machine or plan a mixing process. The significance of the scale and intensity of segregation in the context of chemical reactors will be discussed below. In contrast to this treatment of local texture, the classical residence time distribution paper [I] was concerned with the characterisation of the flow pattern in a continuously operated device and especially with backmixing. The large scale fluid dynamics are primarily convective and are not directly related to mixing on the molecular scale and the associated intensity of segregation. Questions of residence time distribution are therefore treated in a separate article. Although considerations of the local texture of finegrained mixtures apply for example to aerosols, emulsions, precipitates, pigments and many other non-reactive systems, they apply in particular on the molecular scale, i.e. to chemical reactions in inhomogeneous mixtures. (The prefix micro was used by Van Krevelen [4] in this context, whereas Danckwerts wrote of mixing on the molecular scale.) Danckwerts in two papers appearing in 1958 again set the course of much subsequent research. Already in 1953 the intensity of segregation at the molecular scale had been related to the observable rate of a second order reaction taking place between reagents, which were initially present in separate streams (31. Thus. in the limit, no reaction can occur when segregation is complete and the rate attains its maximum value when the mixture is chemically uniform. Any segregation present must therefore retard reaction. The 1958 paper
1950s The literature of the 1940s and the early 1950s reveals little research into mixing, but rather for example into distillation, liquid extraction and the then new technique of fluidisatioo. Mixing research consisted of applying the methods of engineering fluid mechanics to stirred tanks. The drag on an impeller was considered and the power number-Reynolds number curves of many industrially used stirrers were determined, notably by Rushton et al. The pumping capacity of an impeller, the total flow circulating in a tank and the role of batlIes in vortex suppression and turbulence generation were investigated. The year 1953 marked, however, a turning point. Danckwerts published not only his celebrated paper on residence time distribution [l], but also two papers addressing themselves to the quality of mixing [2] (what do we mean when we say that something is mixed?) srnd its quantitative difioition and determination [3] (how is goodness of mixing to be determined?). Many concepts and definitions, which have since become classical, were introduced. The review “Theory of Mixtures and Mixing” [Z] expressed our notion of the scale of scrutiny as follows: “Unless the reasons for making up a mixture are known, it is impossible to decide whether it is well or badly mixed. Any mixture, if scrutinized closely enough, will show regions of segregation-that is, the composition will vary from point to point. The size of the regions of segregation which can be tolerated will vary from one case to another. The term “scale of scrutiny” will be applied here to the minimum size of the regions of segregation in #he mixture which would cause it to be regarded as imperfectly mixed for a specified purpose. Defined in this imprecise way, the scale of scrutiny can only be expressed as an order of magnitude (length, volume or area), but the concept is a useful one.” The probably better known paper “The definition and measurement of some characteristics of mixtures” [3] considered the local texture of a non-uniform mixture. (The only important restriction is that this mixture shall be fine-grained, i.e. the scale of scrutiny shall encompass a large number of particles (ions, molecties etc.) of each component e.g. solutions and mixtures of gases. When fully randomized such a mixture will be essentially uniform in composition). Two quantities characterising finegrained mixtures were defined, the scale and intensity of segregation. Roughly speaking these express the extent and amount of variability of the local property (e.g. me
5
6
J. R.
“The effect of incomplete mixing on homogeneous reactions” [5] revealed that when a second order reaction is used as a chemical tracer to measure the intensity of segregation, the reaction should be slow enough that practically no reagent is consumed in the This restriction reactor. often produces contradiction, since slow reactions cause little segregation. The situation where a single feed stream, containing all necessary reagents, enters a reactor and mixes with its contents was also treated by Danckwerts [S]. This results in dilution of the fresh reagents and therefore in a retardation of reaction. That mixing can either accelerate or retard reaction, depending upon whether the reagents enter the reactor separately or pre-mixed respectively, was clearly recognized by Danckwerts [5], has however caused some confusion in the literature. Thus some writers use the terms species mixing and self mixing (age mixing) respectively to distinguish the two cases, although the same mechanism (mixing on the molecular scale) is operative in both. In 1958 Danckwerts also published “Measurement of molecular homogeneity in a mixture” [6] giving a method which has been developed and widely applied by Hiby et al. [7]. In essence Danckwerts showed how to use a diffusion controlled reaction (e.g. neutralisation) to determine the intensity of segregation. The limitations inherent in this approach are not experimental, but relate to the significance of the intensity of segregation. For example, suppose it has been measured and a different, slower reaction is to be carried out in the same apparatus under the same hydrodynamic conditions. The segregation will be lower, but there is no way of predicting it from the acid/base measurements. The difficulty is that the intensity of segregation depends upon the interaction between the diffusional flux and the reaction kinetics (see next Section). It is a characterising variable, unrelated to the underlying transport phenomena. By the end of the 1950s backmixing, species mixing, self-mixing, segregation etc. had been thought out by Danckwerts, perhaps in moments of “academic indolence” [S]. and had started to enter into the conciousness of many chemical engineers. To a large extent Danckwerts left the development of new theories of mixing and the treatment of more complex problems, e.g. precipitation, nucleation, combustion, selectivity in multiple reactions, to others. He pursued his other line of research, gas absorption especially when accompanied by chemical reaction [9]. And yet is it so other? The absorption of a gas by a liquid is not only formally analogous to the mixing of separate feed streams in a reactor. It relies on the same mass transfer mechanisms and the concentration gradients set up produce the same effects, namely a reduction in rate and possibly a modification of selectivity relative to the state of homogeneity on the molecular scale. PERSPECTIVES M MICROhiawG
The 1960s During this period several experimental studies sought to decide if the continuous stirred tank reactor operating with a single feed stream was best described as
BOURNE
homogeneous, fully segregated [S] or partially segregated. This was directly inspired by Ref. [5]. The results were, however, inconclusive. The stirrer speeds and feed positions used were so abnormal that the residence time distribution deviated from good mixing and the measured rise in conversion could seldom be attributed unequivocally to inhomogeneity at the molecular scale. In retrospect it seems that the reactions were too slow and the solvents insufficiently viscous to induce segregation. Duckwerts’ ideas about segregation in reactors [5] also set off attempts to model partial segregation, most effort being devoted to the single feed stream case. The topic of micromixing began to become divorced from reality for the following reasons: (a) most models lacked a physical (e.g. fluid mechanical) basis: (b) the model parameters were seldom known independently, but rather were fitted, and this established nothing and (c) the limits of conversion between homogeneous and completely segregated mixtures are widest for the continuous, well-mixed tank reactor and yet amount to at most 7% for a second order reaction. (Multiple reactions can exhibit somewhat wider limits, but were not intensively studied during the 1%0’s). Apart from polymerization, where particularly the termination step of addition reactions can be diffusion controlled (NorrishTromsdorf effect), the risk of solving a non-problem was great. The Proceedings of the international meetings on Chemical Reaction Engineering also reveal this. The 1970s and 1980s It now seems clear that: (a) inhomogeneity at the molecular scale develops if the half-life time which would be required by chemical reaction in a homogeneous solution is of the same order as or less than the half-life time for micromixing in the absence of reaction [lo, 121; (b) micromixing proceeds by molecular diffusion in small fluid elements which are being gradually strained [M-13]. The way in which these conclusions have been reached wiU now be outlined. Two miscible solutions, each containing one of the reagents A and B, are to be mixed in turbulent flow. Suppose that the B-rich solution is much more concentrated, so that less of it must be used to obtain a given stoichiometric ratio. Mixing consists initially of convective or flow-dominated processes, namely distribution and turbulent dispersion, whereby fresh, B-rich fluid elements are deformed until their scale of segregation is comparable to the Kolmogoroff velocity microscale. Mixing continues below this scale by molecular diffusion, which reduces the intensity of segregation, and also by laminar strain, which reduces the scale further and accelerates diffusion [lo, 121. Quantitative modelling consists of the unsteady state diffusion equation with a convective term for the simultaneous shrinkage of the fluid element. First estimates of the initial size and the rate of deformation can be obtained from the energy dissipation rate and the kinematic viscosity [l&12]. Use of diffusion-reaction equations to describe the course of a reaction during micromixing leads to the second Damkoehler number (or what elsewhere we have termed the mixing modulus [lCl]),
7
Mixing on the molecular scale (micromixing) which is proportional to the ratio of the diffusion time to the reaction time, i.e. its value indicates whether the reaction regime is slow (controlled by kinetics), fast (kinetics and ditfusion both important) or instantaneous (fully diffusion controlled). Fast reactions in a single phase, the inlluence of pore diffusion on reaction rates in porous catalysts (Thiele modulus) and the retardation of the rate of a gas/liquid reaction by diffusion through the liquid film (Hatta number [9] is proportional to the square root of the ratio of the diffusion and reaction times) are today all described by the same principles. APPLICATIONS
In turbulent aqueous solutions it is readily shown that only reactions having half-lives of less than around 0.1 s are likely to take place under conditions of partial segregation. Clearly a pre-mixed feed stream will not be used for such reactive materials and only the separate feed stream case is relevant. A fast single second order reaction will then be retarded by segregation, but the resultant loss of conversion can frequently be compensated by an increase in the reactor volume. Fast multiple reactions, whose product distribution depends upon mixing on the molecular scale, produce a different product spectrum when segregation occurs. This wastes raw materials and complicates the separation following the reactor. It cannot moreover be compensated by changing reactor volume. Thus the effect of segregation upon some multiple reactions is likely to be economically and ecologically more serious than when conducting a single reaction. 114. 151; (b) Examples include: (a) copolymerization autocatalytic reactions [16, 173; (c) competitive, consecutive reactions, where changes of selectivity caused by segregation of up to two orders of magnitude have been measured, e.g. single phase nitrations [18, 191, brominations [20,21] and iodinations [22,23] of aromatic compounds, as well as some diazo couplings [24-261. These substitutions exhibited the maximum yield of the intermediate in a reaction sequence in the slow reaction regime and a drastic loss of yield towards the instantaneous regime. In some examples even isomer distributions depended upon segregation [20,27]. Almost all the results obtained with these reactions are qualitatively consistent with the mechanism of mixing on the molecular scale outlined above. In those few cases where sticient information on reaction mechanism, kinetics, reactor configuration etc. was available, good quantitative agreement has also been obtained [IO-121. TWO-PEASE
REACTIONS AND MICBOMCUNG
Fast single phase reactions and two phase reactions have been described by diffusion-reaction equations as noted above. The purpose of this short section is to stress the similarity of the effect of mixing on product distribution in the two cases. Parallel reactions e.g. alkylation and competitive, two-phase [28,291 nitration of benzene and toluene [30.43]: the results for these two-phase systems are qualitatively the same as for homogeneous reactions (31). Competitive, consecutive reactions, e.g. chlorination of
hydrocarbons [32-341, of p-cresol[35-371 and of acetone [38] and sulphonation of benzene [39, 401: in all cases less intensive mixing, denoted by a fall in the liquid film mass transfer coefficient and thus an increase in the diffusion path length, caused a lower yield of intermediate. This trend is the same as that observed with fast, single phase reactions and was typically caused by the second reaction in the lilm becoming fast. A fine example of the applicability of diffusion-reaction theory to the chlorination of p-cresol has been given by Pangarkar and Sharma [37]. In the experimental part of this study all requisite physico-chemical quantities were determined independently (solubility and diiusivity of chlorine, rate constant of each of the two chlorination& and the liquid film mass transfer coefficient). Three different reaction regimes were predicted and also realized, whereby the selectivity for the monochloro-derivative varied over one order of magnitude. Provided sufficient physico-chemical data are known, product distributions from fast, homogeneous and heterogeneous reactions can now be predicted with suflicient accuracy for many purposes. THEFUTURE
Ten years ago few convincing examples of mixingcontrolled product distributions were knowu. Experimental and theoretical research has now established such phenomena. With the symptoms becoming clearer, it is likely that further examples will be recognized and further improvements in selectivity will be attained. A likely field for advances is polymerization [41]. Evidence of the large effect of viscosity on micromixing exists (25, 421, whereas macromixing in the turbulent regime is scarcely dependent upon viscosity. The new model of micromixing should be applied to predicting the effect of viscosity on polymerization, and attention paid to the possible simultaneous development of temperature segregation in viscous fluids. Many enzyme catalysed reactions are very rapid and bacteria and other micro-organisms are around one order of magnitude smaller than the Kolmogoroff eddies. The mechanism of micromixiug will therefore also be relevant for reaction and mass transfer [44] at such scales. Perhaps the dependence of yield in some fermentations upon agitation conditions will be explicable and quantitatively describable in terms of micromixing. With fast reactions the feed stream can start to react locally before it has been mixed on the molecular scale with the whole reactor contents and this can be detrimental to selectivity or even dangerous. Now that chemical tracers sensitive to micromixing are available, they can be used to improve the design and location of feed ports. “It is important to discover how much of the energy supplied to the mixer is essential and how much is dissipated fruitlessly” [2]. Since 1953 much has been learned about this matter in the fields of gas dispersion, heat transfer and partMe suspension in stirred tanks. The newly emerging mechanism of micromixing predicts: (a) a scale-up criterion of constant power per unit volume for the rate of mixii at the molecular scale; and (b) all mixing devices operated at the same power per
8
I. R. BOURNE
unit volume will generate the same rate of micromixing. Evidence on these two matters will accumulate and generate new guidelines about “absolute energetic efficiencies” [2] in the context of mixing on the molecular SC& REFERENCES
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