Theoretical Models of Single Droplet Drying Kinetics: A Review

REFERENCES

• Masters , K. Spray Drying: An Introduction to Principles, Operational Practice and Applications ; Leonard Hill Books : London , 1972 .
   Google Scholar
• Mujumdar , A.S. , Ed. Handbook of Industrial Drying ; CRC Press : Boca Raton , FL , 2007 .
   Google Scholar
• Charlesworth , D.H. ; Marshall , W.R. , Jr. Evaporation from drops containing dissolved solids . AIChE Journal 1960 , 6 ( 1 ), 9 – 23 .
   Web of Science ®Google Scholar
• Strongin , V. ; Borde , I. A mathematical model of convective drying incorporating sorption isotherms . In Advances in Drying , Vol. 4 ; Mujumdar , A.S. , Ed.; Hemisphere : New York , 1987 ; 249 – 278 .
   Google Scholar
• Kuts , P.S. ; Strumiłło , C. ; Zbiciński , I. Evaporation kinetics of single droplets containing dissolved biomass . Drying Technology 1996 , 14 ( 9 ), 2041 – 2060 .
   Web of Science ®Google Scholar
• Fyhr , C. ; Kemp , I.C. Comparison of different drying kinetics models for single particles . Drying Technology 1998 , 16 ( 7 ), 1339 – 1369 .
   Web of Science ®Google Scholar
• Langrish , T.A.G. ; Kockel , T.K. The assessment of a characteristic drying curve for milk powder for use in computational fluid dynamics . Chemical Engineering Journal 2001 , 84 ( 1 ), 69 – 74 .
   Web of Science ®Google Scholar
• Sano , Y. ; Keey , R.B. The drying of a spherical particle containing colloidal material into a hollow sphere . Chemical Engineering Science 1982 , 37 ( 6 ), 881 – 889 .
   Web of Science ®Google Scholar
• Abuaf , N. ; Staub , F.W. Drying of liquid-solid slurry droplets . In Drying '86 , Vol. 1 ; Mujumdar , A.S. , Ed.; Hemisphere : Washington , DC , 1986 ; 277 – 284 .
   Google Scholar
• Ferrari , G. ; Meerdink , G. ; Walstra , P. Drying kinetics for a single droplet of skim-milk . Journal of Food Engineering 1989 , 10 , 215 – 230 .
   Web of Science ®Google Scholar
• Nešić , S. The evaporation of single droplets—Experiments and modelling . In Drying '89 ; Mujumdar , A.S. , Roques , M. , Eds.; Hemisphere : New York , 1990 ; 386 – 393 .
   Google Scholar
• Nešić , S. ; Vodnik , J. Kinetics of droplet evaporation . Chemical Engineering Science 1991 , 46 ( 2 ), 527 – 537 .
   Web of Science ®Google Scholar
• Borde , I. ; Zlotnitsky , A. Drying and Combustion of Solid–Liquid Slurry Droplets ; Annual Report; Ben-Gurion University of the Negev : Israel , 1991 .
   Google Scholar
• Levi-Hevroni , D. ; Levy , A. ; Borde , I. Mathematical modelling of drying of liquid/solid slurries in steady state one-dimensional flow . Drying Technology 1995 , 13 ( 5–7 ), 1187 – 1201 .
   Web of Science ®Google Scholar
• Elperin , T. ; Krasovitov , B. Evaporation of liquid droplets containing small solid particles . International Journal of Heat and Mass Transfer 1995 , 38 ( 12 ), 2259 – 2267 .
   Web of Science ®Google Scholar
• Dolinsky , A.A. High-temperature spray drying . Drying Technology 2001 , 19 ( 5 ), 785 – 806 .
   Web of Science ®Google Scholar
• Mezhericher , M. ; Levy , A. ; Borde , I. Theoretical drying model of single droplets containing insoluble or dissolved solids . Drying Technology 2007 , 25 ( 6 ), 1025 – 1032 .
   Web of Science ®Google Scholar
• Mezhericher , M. ; Levy , A. ; Borde , I. Modelling of particle breakage during drying . Chemical Engineering and Processing: Process Intensification 2008 , 47 ( 8 ), 1404 – 1411 .
   Web of Science ®Google Scholar
• Mezhericher , M. ; Levy , A. ; Borde , I. Heat and mass transfer of single droplet/wet particle drying . Chemical Engineering Science 2008 , 63 ( 1 ), 12 – 23 .
   Web of Science ®Google Scholar
• Seydel , P. ; Sengespeick , A. ; Blomer , J. ; Bertling , J. Experiment and mathematical modeling of solid formation at spray drying . Chemical Engineering and Technology 2004 , 27 ( 5 ), 505 – 510 .
   Web of Science ®Google Scholar
• Seydel , P. ; Blomer , J. ; Bertling , J. Modelling particle formation at spray drying using population balance . Drying Technology 2006 , 24 , 137 – 146 .
   Web of Science ®Google Scholar
• Handscomb , C.S. ; Kraft , M. ; Bayly , A.E. A new model for the drying of droplets containing suspended solids after shell formation . Chemical Engineering Science 2009 , 64 ( 2 ), 228 – 246 .
   Web of Science ®Google Scholar
• Handscomb , C.S. ; Kraft , M. ; Bayly , A.E. A new model for the drying of droplets containing suspended solids . Chemical Engineering Science 2009 , 64 ( 4 ), 628 – 637 .
   Web of Science ®Google Scholar
• Chen , X.D. ; Lin , S.X.Q. Air drying of milk droplet under constant and time-dependent conditions . AIChE Journal 2005 , 51 ( 6 ), 1790 – 1799 .
   Web of Science ®Google Scholar
• Lin , S.X.Q. ; Chen , X.D. A model for drying of an aqueous lactose droplet using the reaction engineering approach . Drying Technology 2006 , 24 ( 11 ), 1329 – 1334 .
   Web of Science ®Google Scholar
• Lin , S.X.Q. ; Chen , X.D. A reaction engineering approach to modelling the cream and whey protein concentrate droplet drying . Chemical Engineering and Processing 2007 , 46 ( 5 ), 437 – 443 .
   Web of Science ®Google Scholar
• Patel , K.C. ; Chen , X.D. Surface-centre temperature differences within milk droplets during convective drying and drying-based Biot number analysis . AIChE Journal 2008 , 54 , 3273 – 3290 .
   Web of Science ®Google Scholar
• Patel , K.C. ; Chen , X.D. ; Lin , S.X.Q. A composite reaction engineering approach to drying of aqueous droplets containing sucrose, maltodextrin (DE6) and their mixtures . AIChE Journal 2009 , 55 ( 1 ), 217 – 231 .
   Web of Science ®Google Scholar
• Keey , R.B. Drying of Loose and Particulate Materials ; Hemisphere Publishing : New York , 1992 .
   Google Scholar
• van der Lijn , J. Simulation of heat and mass transfer in spray drying . Agricultural Research Reports 1976 , 845 , 72 – 85 .
   Google Scholar
• Chen , X.D. The basis of a REA to modelling air-drying of small droplets or thin layer materials . Drying Technology 2008 , 26 ( 6 ), 627 – 639 .
   Web of Science ®Google Scholar
• Patel , K.C. ; Chen , X.D. Prediction of spray-dried product quality using two simple drying kinetics models . Journal of Food Process Engineering 2005 , 28 ( 6 ), 567 – 594 .
   Web of Science ®Google Scholar
• Cheong , H.W. ; Jeffreys , G.V. ; Mumford , C.J. A receding interface model for the drying of slurry droplets. AIChE Journal 1986, 32 (8), 1334–1346.
   Web of Science ®Google Scholar
• Minoshima , H. ; Matsushima , K. ; Liang , H. ; Shinohara , K. Basic model of spray drying granulation . Journal of Chemical Engineering of Japan 2001 , 34 ( 4 ), 472 – 478 .
   Web of Science ®Google Scholar
• Minoshima , H. ; Matsushima , K. ; Liang , H. ; Shinohara , K. Estimation of diameter of granule prepared by spray drying of slurry with fast and easy evaporation . Journal of Chemical Engineering of Japan 2002 , 35 ( 9 ), 880 – 885 .
   Web of Science ®Google Scholar
• Yarin , A.L. ; Brenn , G. ; Kastner , O. ; Tropea , C. Drying of acoustically levitated droplets of liquid–solid suspensions: Evaporation and crust formation . Physics of Fluids 2002 , 14 ( 7 ), 2289 – 2298 .
   Web of Science ®Google Scholar
• Yarin , A.L. ; Brenn , G. ; Kastner , O. ; Rensink , D. ; Tropea , C. Evaporation of acoustically levitated droplets . Journal of Fluid Mechanics 1999 , 399 , 151 – 204 .
   Web of Science ®Google Scholar
• Liang , H. ; Shinohara , K. ; Minoshima , H. ; Matsushima , K. Analysis of constant rate period of spray drying of slurry . Chemical Engineering. Science 2001 , 56 , 2205 – 2213 .
   Web of Science ®Google Scholar
• Fan , L.S. ; Zhu , C. Principles of Gas-Solid Flows ; Cambridge University Press : New York , 1998 .
   Google Scholar
• Chen , X.D. Air drying of food and biological materials: Modified Biot and Lewis number analysis . Drying Technology 2005 , 23 ( 9–11 ), 2239 – 2248 .
   Web of Science ®Google Scholar
• Patel , K.C. ; Chen , X.D. ; Kar , S. The temperature uniformity during air drying of a colloidal liquid droplet . Drying Technology 2005 , 23 ( 12 ), 2337 – 2367 .
   Web of Science ®Google Scholar
• Mezhericher , M. ; Levy , A. ; Borde , I. Heat and mass transfer and breakage of particles in drying processes . Drying Technology 2009 , 27(7–8) , 870 – 877 .
   Web of Science ®Google Scholar
• Marshall , W.R. , Jr. Heat and mass transfer in spray drying . Transactions of the ASME , 1955 , 77 , 1377 – 1385 .
   Google Scholar
• Furuta , T. ; Hayashi , H. ; Ohashi , T. Some criteria of spray dryer design for food liquid . Drying Technology 1994 , 12 ( 1–2 ), 151 – 177 .
   Web of Science ®Google Scholar
• Ali , H.H. ; Mumford , C.J. ; Jeffreys , G.V. ; Bains , G.S. A study of evaporation from, and drying of, single droplets . In Drying '89 ; Mujumdar , A.S. , Ed.; Hemisphere : New York , 1990 ; 378 – 385 .
   Google Scholar
• Trommelen , A.M. ; Crosby , E.J. Evaporation and drying of drops in superheated vapours . AIChE Journal 1970 , 16 ( 5 ), 857 – 867 .
   Web of Science ®Google Scholar
• Hecht , J.P. ; King , C.J. Spray drying: influence of developing drop morphology on drying rates and retention of volatile substances. 2. Modelling . Industrial and Engineering Chemistry Research 2000 , 39 ( 6 ), 1766 – 1774 .
   Web of Science ®Google Scholar
• Hecht , J.P. ; King , C.J. Spray drying: Influence of developing drop morphology on drying rates and retention of volatile substances. 1. Single-drop experiments . Industrial and Engineering Chemistry Research 2000 , 39 ( 6 ), 1756 – 1765 .
   Web of Science ®Google Scholar
• Frey , D.D. ; King , C.J. Experimental and theoretical investigation of foam-spray drying. 1. Mathematical model for the drying of foams in the constant-rate period . Industrial and Engineering Chemistry Fundamentals 1986 , 25 ( 4 ), 723 – 730 .
   Web of Science ®Google Scholar
• Walton , D. ; Mumford , C. The morphology of spray-dried particles—The effect of process variables upon the morphology of spray-dried particles . Transactions of the Institute of Chemical Engineers, Part A 1999 , 77 , 442 – 460 .
   Google Scholar
• Thijssen , H.A.C. ; Ruikens , W.H. Retention of aroma in drying liquid foods . De Ingenieur (The Hague) 1968 , 80 , 45 – 56 .
   Google Scholar
• Menting , L.C. Retention of volatiles during the air drying of aqueous carbohydrate solutions . Ph.D. dissertation , Eindhoven University of Technology , Eindhoven , The Netherlands , 1969 .
   Google Scholar
• Wijlhuizen , A.E. ; Kerkhof , P.J.A.M. ; Bruin , S. Theoretical study of the inactivation of phosphatase during spray drying of skim milk . Chemical Engineering Science 1979 , 34 , 651 – 660 .
   Web of Science ®Google Scholar
• Crosby , E.J. ; Weyl , R.W. Foam Spray Drying: General Principles . AIChE Symposium Series, No. 163 , vol. 73 , 1977 , 82 – 94 .
   Google Scholar
• Wallack , D.A. ; El-Sayed , T.M. ; King , C.J. Changes in particle morphology during drying of drops of carbohydrate solutions and food liquids. 2. Effects of drying rate . Industrial and Engineering Chemistry Research 1990 , 29 ( 12 ), 2354 – 2357 .
   Web of Science ®Google Scholar
• Frey , D.D. ; King , C.J. Experimental and theoretical investigation of foam-spray drying. 2. Experimental investigation of volatiles loss during foam-spray drying . Industrial and Engineering Chemistry Fundamentals 1986 , 25 ( 4 ), 730 – 735 .
   Web of Science ®Google Scholar
• Sloth , J. ; Kiil , S. ; Jensen , A.D. ; Andersen , S.K. ; Jorgensen , K. ; Schiffter , H. ; Lee , G. Model based analysis of the drying of a single solution droplet in an ultrasonic levitator . Chemical Engineering Science 2006 , 61 , 2701 – 2709 .
   Web of Science ®Google Scholar
• Walton , D. ; Mumford , C. Spray dried products—Characterization of particle morphology . Transactions of the Institute of Chemical Engineers, Part A 1999 , 77 , 21 – 38 .
   Google Scholar
• Brenn , G. ; Wiedemann , T. ; Rensink , D. ; Kastner , O. ; Yarin , A.L. Modelling and experimental investigation of the morphology of spray dried particles . Chemical Engineering and Technology 2001 , 24 , 1113 – 1116 .
   Web of Science ®Google Scholar
• Abramzon , B. ; Sirignano , W.A. Droplet vaporization model for spray combustion calculations . International Journal of Heat and Mass Transfer 1989 , 32 , 1605 – 1618 .
   Web of Science ®Google Scholar
• Ford , I.J. Models of crystallisation in evaporating droplets . Materials Research Society Symposium Proceedings 1996 , 398 , 637 – 642 .
   Google Scholar
• Adhikari , B. ; Howes , T. ; Lecomte , D. ; Bhandari , B.R. A glass transition temperature approach for the prediction of the surface stickiness of a drying droplet during spray drying . Powder Technology 2005 , 149 , 168 – 179 .
   Web of Science ®Google Scholar
• Adhikari , B. ; Howes , T. ; Bhandari , B.R. Use of solute fixed coordinate system and method of lines for prediction of drying kinetics and surface stickiness of single droplet during convective drying . Chemical Engineering and Processing 2007 , 46 , 405 – 419 .
   Web of Science ®Google Scholar
• Van der Lijn , J. ; Kerkhof , P.J.A.M. ; Rulkens , W.H. Droplet heat and mass transfer under spray-drying conditions . In Proceedings of the International Symposium on Heat and Mass Transfer Problems in Food Engineering ; Wageningen , The Netherlands , 1972 ; Paper F3 .
   Google Scholar
• Yarin , A.L. ; Brenn , G. ; Rensink , D. Evaporation of acoustically levitated droplets of binary liquid mixtures . International Journal of Heat and Fluid Flow 2002 , 23 , 471 – 486 .
   Web of Science ®Google Scholar
• Jayanthi , G.V. ; Zhang , S.C. ; Messing , G.L. Modelling of solid particle formation during solution aerosol thermolysis . Aerosol Science and Technology 1993 , 19 , 478 – 490 .
   Web of Science ®Google Scholar
• Eslamian , M. ; Ahmed , M. ; Ashgriz , N. Modelling of nanoparticle formation during spray pyrolysis . Nanotechnology 2006 , 17 , 1674 – 1685 .
   PubMed Web of Science ®Google Scholar
• Eslamian , M. ; Ahmed , M. ; Ashgriz , N. Modelling of solution droplet evaporation and particle evolution in droplet-to-particle spray methods . Drying Technology 2009 , 27 ( 1 ), 3 – 13 .
   Web of Science ®Google Scholar
• Parti , M. ; Paláncz , B. Mathematical model for spray drying . Chemical Engineering Science 1974 , 29 , 355 – 362 .
   Web of Science ®Google Scholar
• Farid , M. A new approach to modelling of single droplet drying . Chemical Engineering Science 2003 , 58 ( 13 ), 2985 – 2993 .
   Web of Science ®Google Scholar
• Dalmaz , N. ; Ozbelge , H.O. ; Eraslan , A.N. ; Uludag , Y. Heat and mass transfer in drying of a suspension droplet: A new computational model . Drying Technology 2007 , 25 , 391 – 400 .
   Web of Science ®Google Scholar
• Handscomb , C.S. ; Kraft , M. ; Bayly , A.E. A New Model for the Drying of Droplets Containing Suspended Solids ; Technical Report 50, c4e-Preprint Series; University of Cambridge , Cambridge , UK , 2007 .
   Google Scholar
• Handscomb , C.S. ; Kraft , M. ; Bayly , A.E. A New Model for the Drying of Droplets Containing Suspended Solids after Shell Formation ; Technical Report 59, c4e-Preprint Series; University of Cambridge, Cambridge , UK , 2008.
   Google Scholar
• Werner , S.R.L. Air Suspension Coating of Dairy Powders: A Micro-Level Process Approach ; Ph.D. thesis , Massey University , Palmerston North , New Zealand , 2005 .
   Google Scholar
• Griffith , J.D. ; Bayly , A.E. ; Johns , M.L. Magnetic resonance studies of detergent drop drying . Chemical Engineering Science 2008 , 63 ( 13 ), 3449 – 3456 .
   Web of Science ®Google Scholar
• Handscomb , C.S. ; Kraft , M. Simulating the Structural Evolution of Droplets Following Shell Formation . Technical Report 63, c4e-Preprint Series ; University of Cambridge , Cambridge , UK , 2008 .
   Google Scholar
• Mezhericher , M. ; Levy , A. ; Borde , I. The influence of thermal radiation on drying of single droplet/wet particle . Drying Technology 2008 , 26 ( 1 ), 78 – 89 .
   Web of Science ®Google Scholar
• Lin , S.X.Q. ; Chen , X.D. Improving the glass-filament method for accurate measurement of drying kinetics of liquid droplets . Transactions of IChemE Part A – Chemical Engineering Research and Design 2002 , 80 , 401 – 410 .
   Web of Science ®Google Scholar
• Chen , X.D. ; Peng , X.F. Modified Biot number in the context of air drying of small moist porous objects . Drying Technology 2005 , 23 ( 1–2 ), 83 – 103 .
   Web of Science ®Google Scholar
• Rumpf , H. The strength of granules and agglomerates . In Agglomeration ; Knepper , W.A. , Ed.; John Wiley & Sons : New York , 1962 ; 379 – 418 .
   Google Scholar