Abstract
This chapter attempts a general and unifying treatment from a chemical reaction engineering viewpoint, in which the Lagrangian approach is used to describe mixing in a transport process primarily in continuous crystallizer systems. A rational approach to crystallizer description and design requires a solution of the relevant conservation equations representing crystal population and mass and energy balances, together with a description of the kinetics of rate processes involved and a definition of flow patterns within the vessels. The performance of a crystallizer system depends not only on the pertinent intrinsic kinetics of growth and nucleation processes, but also on the physical processes occurring in the vessel (Figure 102).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Abegg, C. F. and Balkrishnan, N. S., “The tanks-in-series concept as a model for imperfectly mixed crystallizers,” Chem. Eng. Prog. Symp. Ser. No. 110 67, 88–96 (1971).
Angst, W. J., Bourne, J. R. and Sharma, R. N., “Mixing and fast chemical reactions. IV: The dimensions of the reactions zone,” Chem. Eng. Sci. 37, 585–590 (1982a).
Angst, W. J., Bourne, J. R. and Sharma, R. N., “Mixing and fast chemical reactions V: Influence of diffusion with reaction zone on selectivity,” Chem. Eng. Sci. 37, 1259–1264 (1982b).
Apostolopoulos, G. P. and Smith, Jr. W. D., “A new model for micromixing in chemical reactors,” International Symposium on Reaction Engineering—4 (ISCRE4), Heidelberg (April, 1976).
Asbjornsen, A. O., “Incomplete mixing simulated by fluid flow network,” AIChE-ICE Symp. Ser. No. 10, 40-49(1965).
Askew, W. S. and Beckman, R. B., “Heat and mass transfer in an agitated vessel,” Ind. Eng. Chem. Proc. Des. Dev. 4, 311–318 (1965).
Aubry, C. and Villermaux, J., “Representation du mèlange imparfait de deux courants de réactif dans un réacteur agité continu,” Chem. Eng. Sci. 30, 457–464 (1975).
Baldyga, J. and Bourne, J. R., “Mixing and fast chemical reaction. VIII: Initial deformation of material elements in isotropic homogeneous turbulence,” Chem. Eng. Sci. 39, 329–334 (1984a).
Baldyga, J. and Bourne, J. R., “A fluid mechanical approach to turbulent mixing and chemical reaction. I: Inadequacies of available models,” Chem. Eng. Commun. 28, 231–242 (1984b).
Baldyga, J. and Bourne, J. R., “A fluid mechanical approach to turbulent mixing and chemical reaction. II: Micromixing in the light of turbulence theory,” Chem. Eng. Commun. 28, 243–258 (1984c).
Baldyga, J. and Bourne, J. R., “A fluid mechanical approach to turbulent mixing and chemical reaction. III: Computational and experimental results for the new micromixing model,” Chem. Eng Commun. 28, 259–281 (1984d).
Ballesteros, R. L., Riba, J. P. and Couderc, J. P., “Dissolution of non-spherical particles in solid-liquid fluidization,” Chem. Eng. Sci. 37, 1639–1644 (1982).
Bamforth, A. W., Industrial Crystallization, Leonard Hill, London (1965).
Barker, J. J. and Treybal, R. E., “Mass transfer coefficients for solids suspended in agitated liquids,” AIChEJ. 6, 289–295 (1960).
Barthole, J. P., David, R. and Villermaux, J., “A new chemical method for the study of local micromixing conditions in industrial stirred tanks,” ACS Symp. Ser. No. 196, 545-554 (1982).
Becker, Jr. G. W. and Larson, M. A., “Mixing effects in continuous crystallization,” Chem. Eng. Prog. Symp. Ser. No. 95 65, 14–23 (1969).
Belvi, H., Bourne, J. R. and Rys, P., “Mixing and fast chemical reaction III: Diffusion reaction model for CSTR,” Chem. Eng. Sci., 36, 1649–1654 (1981).
Bennett, R. C., “Product size distribution in commercial crystallizers,” Chem. Eng. Prog. 58, 76–80 (1962).
Bennett, R. C., Fiedelman, H. and Randolph, A. D., “Crystallizer influenced nucleation,” Chem. Eng. Prog. 69, 86–93 (1973).
Bennett, R. C. and van Buren, M. V, “Commercial urea crystallization,” Chem. Eng. Prog. Symp. Ser. No. 110 67, 44–49 (1969).
Bolzern, O. and Bourne, J. R., “Mixing and fast chemical reaction. VI: Extension of the reaction zone,” Chem. Eng. Sci. 38, 999–1003 (1983).
Boon-Long, S., Laguerie, C. and Coudrec, J. P., “Mass transfer from suspended solids to a liquid in agitated vessels,” Chem. Eng. Sci. 33, 813–819 (1978).
Bourne, J. R. and Rohani, S., “Mixing and fast chemical reaction VII: Deforming reaction zone model for the CSTR,” Chem. Eng Sci. 38, 911–916 (1983).
Bransom, S. H., “Continuous crystallizer design,” Chem. Proc. Eng. 46, 647–657 (1965).
Broadfoot, R. and White, E. T., “Performance charts for continuous pans,” Proc. Qld. Soc. Sugar Cane Tech. (1915).
Buurmann, C., Resoort, G. and Plaschkes, A., “Scaling-up rules for solids suspension in stirred vessels,” Chem. Eng. Sci. 41, 2865–2871 (1986).
Calderbank, P. H. and Jones, S. J. R., “Physical rate processes in industrial fermentation—Part III Mass transfer from fluid to solid particles suspended in mixing vessels,” Trans. Inst. Chem. Eng. 30, 363–368 (1961).
Calderbank, P. H. and Moo-Young, M.B., “Continuous phase heat and mass transfer properties of dispersions,” Chem. Eng Sci. 16, 39–54 (1961).
Chai, C. and Valderrama, J. O., “A new approach to view partial segregation model in chemical reactors,” Chem. Eng. Sci. 37, 494–496 (1982).
Chapman, C. M., Nienow, A. W., Cooke, M. and Middleton, J. C., “Particle-gas-liquid mixing in stirred vessels: Particle-liquid mixing,” Chem. Eng. Res. Des. 61, 71–81 (1983).
Chen, M. S. K. and Fan, L. T., “A reversed two-environment model for micromixing in a continuous flow reactor,” Can. J. Chem. Eng. 49, 704–708 (1971).
Chiang, C. L. and Chen, Y. T., “Comments on the shrinking-aggregate two-environment mixing model,” Chem. Eng. Sci. 46, 1879–1880 (1991).
Costa, P. and Trevissoi, C, “Some kinetic and thermodynamic features of reaction between partially segregated fluids,” Chem. Eng. Sci. 27, 653–668 (1972a).
Costa, P. and Trevissoi, C., “Reactions with non-linear kinetics in partially segregated fluids,” Chem. Eng. Sci. 27, 2041–2054 (1972b).
Curl, R. L., “Dispersed-phase mixing.I: Theory and effects in simple reactors,” AIChEJ. 9, 175–181 (1963).
Danckwerts, P. V, “Continuous-flow system: Distribution of residence times,” Chem. Eng. Sci. 2, 1–18(1953).
Danckwerts, P. V, “The effect of incomplete mixing on homogeneous reactions,” Chem. Eng. Sci. 8, 93–102(1958).
David, R. and Villermaux, J., “Micromixing effects on complex reactions in a CSTR,” Chem. Eng. Sci. 30, 1309–1313(1975).
Davidson, J. F. and Harrison, D., Fluidization, Academic Press, London (1971).
Dohan, L. A. and Weinstein, H., “Generalized recycle reactor model for micromixing,” Ind. Eng. Chem. Fundam. 12, 64–69 (1973).
Dudukovik, M. P., “Micromixing effects on multiple steady states in isothermal chemical reactors,” Chem. Eng. Sci. 32, 985–994 (1977a).
Dudukovik, M. P., “On the use of the generalised recycle model to interpret micromixing chemical reactors,” Ind. Eng. Chem. Fundam. 16, 385–388 (1977b).
Dwivedi, P. N. and Upadhyay, S. N., “Particle-fluid mass transfer in fixed and fluidized bed,” Ind. Eng. Chem. Proc. Des. Dev. 16, 157–165 (1977).
Evangelista, J. J., Katz, S. and Shinnar, R., “Scale-up criteria for stirred tank reactors,” AIChE J. 15, 843–853 (1969).
Fan, L. T., Tsai, B. I, Erickson, L. E., “Simultaneous effects of macromixing and micromixing on growth processes,” AIChE J. 17, 689–696 (1971).
Farmer, R. W. and Beckman, J. R., “Particle size improvement by a countercurrent tower crystallizer,” AIChE J. 32, 1099–1107 (1986).
Fisher, R. R., Glatz, C. E. and Murphy, P. R., “Effects of mixing during acid addition on fractionally precipitated protein,” Biotechnol. Bioeng. 28, 1056–1063 (1986).
Garside, J. and Tavare, N. S., “Mixing, reaction, and precipitation in an MSMPR crystallizer: Effects of reaction kinetics on the limits of micromixing”, in Jancic, S. J. and de Jong, E. J. (Eds.), Industrial Crystallization 84, Elsevier, Amsterdam, 131–136 (1984).
Garside, J. and Tavare, N. S., “Mixing, reaction, and precipitation: Limits of micromixing in an MSMPR crystallizer,” Chem. Eng. Sci. 40, 1485–1493 (1985).
Gillespie, B. B. and Carberry, J. J., “Reactor yield at intermediate mixing levels—An extension of van de Vuss’s analysis,” Chem. Eng. Sci. 21, 472–475 (1966).
Goto, S. and Matsubara, M. A., “A generalised two environment model for micromixing in a continuous flow reactor I: Construction of model.,” Chem. Eng. Sci. 30, 61–70 (1975).
Grootscholten, P. A. M., Solid-Liquid Contacting Industrial Crystallizers and its Influence on Product Distribution, Ph.D. thesis, WTHD 150, Laboratory for Process Equipment, Delft, The Netherlands (1982).
Grootscholten, P. A. M., Asselbergs, C. J., Scrutton, A. and de Jong, E. J., “Effect of crystallizer geometry on crystallizer performance”, in Jancic, S. J. and de Jong, E. J. (Eds.), Industrial Crystallization 81, North-Holland, Amsterdam, 189–197 (1982).
Grootscholten, P. A. M., de Jong, E. J. and Scrutton, A., “Chemical engineering approach to industrial crystallization”, in Proc. 2nd World Cong. Chem. Eng IV, Montreal, 59-62 (1981).
Harriott, P., “Mass transfer to particles: Part I: Suspended in agitated tanks. Part II: Suspended in pipeline,” AIChE J. 8, 93–102 (1962).
Harriott, P., “The growth of ice crystals in a stirred tank,” AIChE J. 13, 755–759 (1967).
Hanley, T. R. and Mischike, R. A., “A mixing model for a continuous stirred tank reactor,” Ind. Eng. Chem. Fundam. 17, 51–58 (1978).
Harnby, N., Edwards, M. F. and Nienow, A. W. (Eds.), Mixing in the Process Industries, Butterworth-Heinemann, Oxford (1992).
Harada, M., Arima, K., Eguchi, W. and Nagata, S., “Micromixing in a continuous flow reactor (coalescence and redispersion models)”, in Memoirs of the Faculty of Engineering, Kyoto University, 24,431 (1962).
Harris, I. J. and Srivastava, R. D., “The simulation of single phase turbulent reactor with incomplete reactant mixing,” Can J. Chem. Eng. 46, 66–69 (1968).
Hendl, G. and Mersmann, A. B., “Fluid dynamics and mass transfer in stirred suspensions,” Chem. Eng. Commun. 13, 23–37 (1981).
Hill, S., “Residence time distribution in continuous crystallizer,” J. Appl. Chem. 20, 300–304 (1970).
Hinze, J. O., Turbulence, McGraw-Hill, New York (1959).
Hsia, M. A. and Tavlarides, L. L., “Simulation analysis of drop breakage, coalescence and micromixing in liquid-liquid stirred tanks,” Chem. Eng. Sci. 26, 189–199 (1983).
Jenson, V. G., “A model for mixing with fast chemical reactions,” Chem. Eng. Sci. 38, 1151–1157 (1983).
Jones, A. J. and Mullin, J. W., “Crystallization kinetics of potassium sulphate in a draft tube agitated vessel,” Trans. I. Chem. Eng 51, 302–308 (1973a).
Jones, A. J. and Mullin, J. W., “The design of a draft tube agitated vessel,” Chem. Ind. 21, April, 387–388 (1973b).
Joshi, J. B., “Solid-liquid fluidized beds: Some design aspects,” Chem. Eng. Res. Des. 61, 143–161 (1983).
Juzaszek, P. and Larson, M. A., “Influence of fines dissolving on crystal size distribution in an MSMPR crystallizer,” AIChE J. 23, 460–468 (1977).
Kafarov, V. V, Ivanov, V. A. and Brodskii, S. Ya., “Recycling in chemical processes,” Int. Chem. Eng. 25,453–473, 617-644 (1985).
Kattan, A. and Alder, R. J., “A stochastic model for homogeneous turbulent tubular reactors,” AIChE J. 13, 580–585 (1967).
Kattan, A. and Alder, R. J., “A conceptual framework for mixing in continuous chemical reactors,” Chem. Eng. Sci. 27, 1013–1028 (1972).
Keey, R. B. and Glen, J. B., “Mass transfer from fixed and freely suspended particles in an agitated vessel,” AIChE J. 12, 401–403 (1966).
Kern, D. Q., Process Heat Transfer, McGraw-Hill, London (1950).
Klein, J. P., David, R. and Villermaux, J., “Interpretation of experimental liquid phase micromixing phenomena in a continuous stirred reactor with short residence times,” Ind. Eng. Chem. Fundam. 19, 373–379 (1980).
Knudsen, J. G., “Fouling of heat exchangers: Are we solving the problems?,” Chem. Eng. Prog. 80, 63–69 (1984).
Kneule, F., “Scale-up in the suspension of solids in agitated vessels,” Int. Chem. Eng. 25, 214–222 (1985).
Komasawa, I., Moriaka, S., Kuboi, R. and Otake, T., “A method of measurement of interaction rates of dispersed phases in a continuous flow stirred tank,” J. Chem. Eng. Jpn., 4, 319–324 (1971).
Komasawa, I., Sasakura, T. and Otake, T., “Behavior of reacting and coalescing dispersed phase in stirred tank reactor,” J. Chem. Eng. Jpn. 2, 208–211 (1969).
Krause, S., “Fouling of heat transfer surfaces by crystallization and sedimentation,” Int. Chem. Eng. 33, 355–401 (1993).
Kunni, D. and Levenspiel, O., Fluidization Engineering, Wiley, New York (1969).
Lal, P., Kumar, S., Upadhyay, S. N. and Upadhya, Y. D., “Solid-liquid mass transfer in agitated Newtonian and non-Newtonian fluids,” Ind. Eng. Chem. Res. 27, 1246–1259 (1988).
Larson, M. A. and Mullin, J. W., “Crystallization kinetics of ammonium sulphate,” J. Crystal Growth 20, 183–191 (1973).
Levins, D. M. and Glastonbury, J. R., “Particle-liquid hydrodynamics and mass transfer in a stirred vessel,” Trans. I. Chem. Eng. 50,32–41, 132-146 (1972).
Liekhus, K. J.and Hanley, T. R., “A shrinking-aggregate two-environment mixing model,” Chem. Eng. Sci. 42, 2069–2074 (1987).
Liu, C. H., Zhang, D. H., Sun, C. G. and Shen, Z. Q., “The modelling and simulation of a multistage crystallizer,” Chem. Eng. J. 46, 9–14 (1991).
Margolis, G., Sherwood, T. K., Brian, P. L. T. and Sarofim, A. F., “The performance of a continuous well stirred ice crystallizer,” Ind. Eng. Chem. Fundam. 10, 439–452 (1971).
Mao, K. W. and Toor, H. L., “A diffusion model for reactions with turbulent mixing,” AIChE J. 16, 49–52(1970).
Marconi, P. F. and Vatistas, N., “Degree of segregation and coalescence rate parameter in the random coalescence model for a stirred reactor,” AIChE J. 29, 513–516 (1983).
McCabe, W. L., “Crystal growth in aqueous solutions,” Ind. Eng. Chem. 21, 30–33, 112-119 (1929).
McCabe, W. L. and Smith, J. C, Unit Operations of Chemical Engineering, 3rd ed., McGraw-Hill, New York (1976).
Mehta, R. V. and Tarbell, J. M., “Four environment models of mixing and chemical reaction. I: Model development,”, AIChE J. 29, 320–329 (1983).
Mehta, R. V. and Tarbell, J. M., “Experimental study of the effect of turbulent mixing on the selectivity of competing reactions,” AIChE J. 33, 1089–1101 (1987).
Mersmann, A. B., Einenkel, W. D. and Kappel, M., “Design and scale-up of mixing equipment,” Int. Chem. Eng. 16, 590–603 (1976).
Methot, J. C. and Roy, P. H., “Segregation effects on homogeneous second-order reactions,” Chem. Eng. Sci. 26, 569–576 (1971).
Miller, D. N., “Scale-up of agitated vessels: mass transfer from suspended solute particles,” Ind. Eng. Chem. Proc. Des. Dev. 10, 365–375 (1971).
Misztal, S., Kolek, A. and Koch, R., “Isotopic method for studying the kinetics of crystal growth,” Kristall und Technik 15, 1261–1267 (1980).
Miyawaki, O., Tsujikkawa, H. and Yuraguchi, Y, “Chemical reactions under incomplete mixing,” J. Chem. Eng. Jpn., 8, 63–68 (1975).
Mullin, J. W. and Garside, J., “Voidage-velocity relationships in the design of suspended-bed crystallizers,” Br. Chem. Eng. 15, 773–775 (1970).
Nabholz, F., Ott, R. J. and Rys, P., “Mixing-disguised chemical selectivity,” in Proc. 2nd Eur. Conf. Mixing 1977, Paper B2, British Hydromechanical Research Association (BHRA), Cranfield, England, B2-B27 (1977).
Nauman, E. B., “The droplet diffusion model for micromixing,” Chem. Eng. Sci., 30, 1135–1140 (1975).
Nauman, E.B., “Residence time distributions and micromixing”, Chem. Eng. Commun. 8, 53–131 (1981).
Nauman, E. B. and Buffham, B. A., Mixing in Continuous Flow Systems, Wiley, New York (1983).
Ng, D. Y. C and Rippin, D. W. T., “The effect of incomplete mixing on conversion in homogeneous reactions,” in Proc. 3rd Eur. Symp. Chem. React. Eng., Amsterdam, Sept. 1964, Pergamon, Oxford 161–165 (1965).
Nienow, A. W., “Suspension of solid particles in turbine agitated baffled vessels,” Chem. Eng. Sci. 23, 1453–1459(1968).
Nienow, A. W. and Miles, D., “The effect of impeller, tank configuration on fluid particle mass transfer,” Chem. Eng. J. 15, 13–24 (1978).
Nishimura, Y and Matsubara, M., “Micromixing theory via the two environment model,” Chem. Eng. Sci. 25, 1785–1797(1970).
Nyvlt, J., Industrial Crystallization from Solutions, Butterworths, London(1971).
Nyvlt, J., Design of Crystallizers, CRC, Boca Raton, Florida (1992).
Nyvlt, J. and Broul, M., “Crystallization using recycle of mother liquor,” Int. Chem. Eng. 19, 547–552(1979).
Nyvlt, J., Moundry, F. and Veverka, V., “Mathematical models of a cascade of ideally agitated crystallizer,” Coll. Czech. Chem. Commun. 38, 1815–1839 (1973).
Nyvlt, J. and Provaznik, L., “Optimization of multichamber crystallizer,” Coll. Czech. Chem. Commun. 44, 1239–1245(1979).
Nyvlt, J., Skrivanek, J. and Moudry, F., “Series of crystallizers with nucleation in all members. A real crystallizer,” Coll. Czech. Chem. Commun. 30, 1759–1770 (1965).
Oldshue, J. Y, Fluid Mixing Technology, McGraw-Hill, New York (1983).
Ottino, J. M., “Lamellar mixing models for structured chemical reactions and their relationship to statistical models: Macromixing and micromixing and the problems of averages,” Chem. Eng. Sci. 35, 1377–1391 (1980).
Ottino, J. M. and Chella, R., “Modelling of rapidly-mixed fast-crosslinking exothermic polymerization,” AIChEJ. 29, 373–382 (1983).
Ottino, J. M. and Chella, R., “Conversions and selectivity modifications due to mixing in unpremixed reactors,” Chem. Eng. Sci. 39, 551–567 (1984).
Ottino, J. M, Ranz, W. E. and Macosko, C. W., “A lamellar model for the analysis of liquid-liquid mixing,” Chem. Eng. Sci. 34, 877–890 (1979).
Ou, J. C, Lee, C. S. and Chen, S. H., “Mixing of chemically reactive fluid by swirling in a tubular reactor,” Chem. Eng. Sci. 38, 1323–1329 (1983a).
Ou, J. C, Lee, C. S. and Chen, S. H., “Mixing and chemical reactions: Chemical selectivity,” Chem. Eng. Sci. 38, 1015–1019 (1983b).
Ou, J. C, Lee, C. S. and Chen, S. H., “Mixing and chemical reactions: Thermal effects,” Chem. Eng. Sci. 39 1735–1739(1984).
Ou, J. C, Lee, C. S. and Chen, S. H., “Mixing induced by flow geometry: Spatial distribution and time evolution of the measures of mechanical mixedness,” Chem. Eng. Sci. 40, 2225–2232 (1985).
Ou, J. J. and Ranz, W. E., “Mixing and chemical reactions: A comparison between fast and slow reactions,” Chem. Eng. Sci. 38, 1005–1013 (1983a).
Ou, J. J. and Ranz, W. E., “Mixing and chemical reactions: Chemical selectivities,” Chem. Eng. Sci. 38 1015–1019 (1983b).
Ou, J. J. and Ranz, W. E., “Mixing and chemical reactions: Thermal effects,” Chem. Eng. Sci. 39, 1735–1739(1984).
Plasari, E., David, R. and Villermaux, J., “Micromixing phenomena in continuous stirred reactors using a Michaelis-Menten reaction in the liquid phase,” ACS Symp. Ser. No. 65, 126-139 (1978).
Pohorecki, R. and Baldyga, J., “New model of micromixing in chemical reactors 1: General development and application to a tubular reactor,” Ind. Eng. Chem. Fundam. 22, 393–405 (1983a).
Pohorecki, R. and Baldyga, J., “New model of micromixing in chemical reactors 2: Application to a stirred tank reactors,” Ind. Eng. Chem. Fundam. 22, 405–410 (1983b).
Pohorecki, R. and Baldyga, J., “The use of a new model of micromixing for determination of crystal size in precipitation,” Chem. Eng. Sci. 38, 77–83 (1983c).
Pudjiono, P. I., Protein Precipitation in a Couette Flow Device, Ph. D. thesis, University of Manchester, Manchester (1992).
Pudjiono, P. I., Tavare, N. S., Garside, J. and Nigam, K. D. P., “Residence time distribution from a continuous Couette flow device,” Chem. Eng. J. 48, 101–110 (1992).
Pudjiono, P.I. and Tavare, N. S., “Residence time distribution analysis from a continuous Couette flow device around critical Taylor number,” Can. J. Chem. Eng. 71, 312–318 (1993).
Ramshaw, C. and Parker, I., “Crystallizer design model of steady state operation,” Trans. I. Chem. Eng. 51, 82–92 (1973).
Randolph, A. D., Size Distribution Dynamics in a Mixed Suspension, Ph. D. thesis, Iowa State University, Ames (1962).
Randolph, A. D., “The mixed suspension, mixed product removal crystallizer as a concept in crystal — lizer design,” AIChE J. 11, 424–430 (1965).
Randolph, A. D., Deepak, C. and Iskander, M., “On the narrowing of particle size distributions in staged vessels with classified product removal,” AIChEJ. 14, 827–830 (1968).
Randolph, A. D. and Larson, M. A., Theory of Paniculate Processes, Academic, New York (1971).
Randolph, A. D. and Rivera, T., “A model for the precipitation of pentaerythritol tetranitrate (PETN),” Ind. Eng. Chem. Process Des. Dev. 17, 182–188 (1978).
Randolph, A. D. and Tan, C, “Numerical design techniques for staged classified recycled crystallizer,” Ind. Eng. Chem. Process Des. Dev. 17, 189–200 (1978).
Randolph, A. D. and White E. T., “Modelling size dispersion in the prediction of crystal size distribution,” Chem. Eng. Sci. 32, 1067–1076 (1977).
Ranz, W. E., “Applications of a stretch model to mixing, diffusion and reaction in laminar turbulent flows,” AlChEJ. 25, 41–47 (1979).
Rao, D. P. and Dunn, I. J., “A Monte Carlo coalescence model for reaction with dispersion in a tubular reactor,” Chem. Eng. Sci. 25, 1275–1282 (1970).
Rao, D. P and Edwards, L. L., “On the diffusion model of Mao and Toor,” AIChE J. 17, 1264–1265 (1971).
Rice, A. W., Toor, H. L. and Manning, F. S., “Scale of mixing in a stirred vessel,” AIChE J. 10, 125–129(1964).
Ring, T. A., “Continuous precipitation of monosized particles with a packed bed crystallizer,” Chem. Eng. Sci. 39, 1731–1734 (1984).
Rippin, D. W. T., “Segregation in two environment models of a partially mixed continuous reactor,” Chem. Eng. Sci. 22, 247–251 (1967a).
Rippin, D. W. T., “The recycle reactor as a model of incomplete mixing,” Ind. Eng. Chem. Fundam. 6, 488–492 (1967b).
Ritchie, B. W., “Simulating the effect of mixing on the performance of unpremixed chemical flow reactor,” Can. J. Chem. Eng. 58, 626–633 (1980).
Ritchie, B. W. and Togby, A. H., “General population balance modelling of unpremixed feed stream chemical reactors: A review,” Chem. Eng. Commun. 2, 249–264 (1978).
Ritchie, B. W. and Togby, A. H., “A three-environment micromixing model for chemical reactors with arbitrary separate feed streams,” Chem. Eng. J. 17, 173–182 (1979).
Roberts, J. E. and Robinson, J. N., “A mathematical study of crystal growth in a cascade of agitators,” Can. J. Chem. Eng. 35, 105–112 (1957).
Rojkowski, Z., “Crystal size distribution from a cascade of mixed tanks,” Kristall und Technik 12, 1121–1138(1977).
Rowe, P. N. and Claxton, K. T., “Heat and mass transfer from a single sphere to fluid flowing through an array,” Trans. I. Chem. Eng. 43, 321–331 (1965).
Schwartzberg, H. G. and Treybal, R. E., “Fluid and particle motion in turbulent stirred tanks,” Ind. Eng. Chem. Fundam. 7, 1–12 (1968).
Shah, Y. T., Gas-Liquid-Solid Reactor Design, McGraw-Hill, New York (1979).
Shain, S. A., “Performance of stirred reactors with dispersed phase mixing,” AIChE J. 12, 806–809 (1961).
Shiloh, K., Sideman, S. and Resnick, W., “Crystallization in a dispersed phase,” Can. J. Chem. Eng. 53, 137–163 (1975).
Shmidt, L. and Shmidt, J., “Mechanism of crystallization in agitated solutions,” Chem. Eng. Commun. 36, 233–250 (1985).
Skrivanek, J. F., Moundry, F. and Nyvlt, J., “Uber kristallisation XX: Verteilungder teilchengrossen in einem realen kristallisar,” Coll. Czech. Chem. Commun. 32, 480–488 (1967).
Skrivanek, J. and Vacek, V., “Crystallisation in a cascade of ideally stirred vessels. Analytical description of moments of distribution function of particle sizes of the crystalline suspension,” Coll. Czech. Chem. Commun. 42, 3144–3149 (1977).
Spielman, L. A. and Levenspiel, O., “A Monte-Carlo treatment for reacting and coalescing dispersed phase system,” Chem. Eng. Sci. 20, 247–254 (1965).
Sykes, P. and Gomezplata, A., “Particle-liquid mass transfer in stirred tanks,” Can. J. Chem. Eng. 45, 189–196(1967).
Szabo, T. T. and Nauman, E. B., “Copolymerization and terpolymerization in continuous nonideal reactors,” AIChE J. 15, 575–584 (1969).
Takao, M. and Murakami, Y, “Evaluation of intensity of segregation of two environment model for micromixing,” J. Chem. Eng. Jpn. 9, 336–338 (1976).
Tavare, N. S., “Growth rate dispersion,” Can. J Chem. Eng. 63, 436–442 (1985).
Tavare, N. S., “Mixing in continuous crystallizers,” AlChE J. 32, 705–732 (1986).
Tavare, N. S., “Micromixing limits in an MSMPR crystallizer,” Chem. Eng. Technol. 12, 1–12 (1989).
Tavare, N. S., “Mixing, reaction and precipitation: Environment mixing models in continuous crystal — lizers-I. Premixed feeds,” Computers Chem. Eng. 16, 923–936 (1992).
Tavare, N. S. and Chivate, M. R., “CSD analysis from a single stage and two stage cascade of MSCPR crystallizer,” Can. J. Chem. Eng. 56, 758–761 (1978).
Tavare, N. S. and Chivate, M. R., “Growth and dissolution kinetics of potassium sulphate crystallized in a fluidized bed crystallizer,” Trans. I. Chem. Eng. 57, 35–42 (1979).
Tavare, N. S. and Chivate, M. R., “CSD analysis from a single stage and two stage cascade of MSMPR crystallizer,” Indian Chem. Eng. 24, T27–T33 (1982).
Tavare, N. S., Garside, J. and Larson, M. A., “CSD analysis from a cascade of MSMPR crystallizers with recycle,” Chem. Eng. Commun. 47, 185–199 (1986).
Terwilinger, J. P. and Wey, J. S., “Design considerations for a multistage cascade crystallizer,” Ind. Eng. Chem. Process Des. Dev. 15, 467–469 (1976).
Treleaven, C. R. and Togby, A. H., “Conversion in reactors having separate reactant feed streams. The state of maximum mixedness,” Chem. Eng. Sci. 26, 1259–1269 (1971).
Treleaven, C. R. and Togby, A. H., “Monte Carlo methods for simulating micromixing in chemical reactors,” Chem. Eng. Sci. 27, 1497–1513 (1972).
Troung, K. T. and Methot, J. C., “Segregation effects on consecutive reaction in CSTR,” Can. J. Chem. Eng. 54, 572–577 (1976).
Tsai, B. I., Fan, L. T., Erickson, L. E. and Chen, S. K., “The reversed two environment model of micromixing and growth processes,” J. Appl. Chem. Biotechnol 21, 307–312 (1971).
Tournie, P., Laguerie, C. and Couderc, J. P., “Correlation for mass transfer between fluidized spheres and a liquid,” Chem. Eng. Sci. 34, 1247–1255 (1979).
Uhl, V. W. and Gray, J. B., Mixing: Theory and Practice, Academic, London (1966).
Valderrama, J. O. and Gordon, A. L., “Mixing effects on homogeneous p-order reactions. A two parameter model for partial segregation,” Chem. Eng. Sci. 34, 1097–1103 (1979).
Valderrama, J. O. and Gordon, A. L., “A two parameter model for partial segregation: Application to flow reactors with pre-and unpremixed feed,” Chem. Eng. Sci. 36, 839–844 (1981).
Van’t Land, C. M. and Wienk, B. G., “Control of particle size in industrial NaCl crystallization”, in Mullin, J. W. (Ed.), Industrial Crystallization, Plenum, New York, 51–60 (1975).
Villermaux, J., “Drop break-up and coalescence. Micromixing effects in liquid-liquid reactors,” in Rodrigues, A. E., Calo, J. M. and Sweed, N. H. (Eds.), Multiphase Chemical Reactors, Vol. I Fundamentals, NATO Advanced Study Institute Ser. No. 51, Sijthoff and Noordhoff, 285-362(1981).
Villermaux, J., “Mixing in chemical reactors,” ACS Symp. Ser. No. 226, 135-186 (1983).
Villermaux, J., “Micromixing phenomena in stirred reactors,” in Encyclopedia of Fluid Mechanics, Gulf Publishing Co., Houston, Texas, 707–771 (1986).
Villermaux, J. and David, R., “Recent advances in the understanding of micromixing phenomena in stirred reactors,” Chem. Eng. Commun. 21, 105–122 (1983).
Villermaux, J. and Zoulalian, A., “Etat de mélange du fluide dans un réacteur continu. A propos d’un modàle de Weinstein et Aider,” Chem. Eng. Sci. 24, 1513–1517 (1969).
Weinstein, H. J. and Aider, R. J., “Micromixing effects in continuous chemical reactors,” Chem. Eng. Sci. 22, 65–75(1967).
Wen, C. Y and Fan, L. T., Models for Flow Systems and Chemical Reactors, Marcel Dekker, New York (1975).
Weng, H. S., “Residence time distribution model for continuous crystallizer,” J. Chem. Eng. Jpn. 13, 407–409(1980).
Winter, B. and Georgi, H., “An extended crystallizer model for the sizing and optimization of crystallizer cascades,” Int. Chem. Eng. 25, 611–616(1985).
Wolff, P. R. and Larson, M. A., “Crystal size distribution from multistage crystallizers,” Chem. Eng. Prog. Symp. Sen No. 110 67, 97–107 (1971).
Zeitlin, M. A. and Tavlarides, L. L., “Fluid-fluid interactions and hydrodynamics in agitated dispersion,” Can. J. Chem. Eng. 50, 207–215 (1972).
Zoulalian, A. and Villermaux, J., “Influence of chemical parameters on micromixing in a continuous stirred tank reactor,” Adv. Chem. Sen Am. Chem. Soc. 133, 348–361 (1974).
Zwietering, T. N., “The degree of mixing in continuous flow systems,” Chem. Eng. Sci. 11, 1–15 (1959).
Zwietering, T. N., “Suspending of solid particles in liquid by agitators,” Chem. Eng. Sci. 8, 244–253(1958).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Tavare, N.S. (1995). Mixing. In: Industrial Crystallization. The Springer Chemical Engineering Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0233-7_10
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0233-7_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4899-0235-1
Online ISBN: 978-1-4899-0233-7
eBook Packages: Springer Book Archive