Physical Interpretation of Solids Drying: An Overview on Mathematical Modeling Research

REFERENCES

• Liapis , A.I. ; Bruttini , R.A. Theory for the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes: Comparison between experimental data and theory . Separation Technology 1994 , 4 , 144 – 155 .
   Web of Science ®Google Scholar
• Jacobs , A.M. ; Grainger , J. Models of visual word recognition-sampling the state of the art . Journal of Experimental Psychology: Human Perception and Performance 1994 , 29 , 1311 – 1334 .
   Google Scholar
• Luikov , A.V. Systems of differential equations of heat and mass transfer in capillary-porous bodies . International Journal of Heat and Mass Transfer 1975 , 18 , 1 – 14 .
   Web of Science ®Google Scholar
• Whitaker , S. Simultaneous heat, mass, momentum transfer in porous media: A theory of drying . Advances in Heat Transfer 1977 , 13 , 119 – 203 .
   Google Scholar
• Boer , R. Theory of Porous Media: Highlights in the Historical Development and Current State ; Springer : Berlin , 2000 .
   Google Scholar
• Barbosa-Canovas , G.V. ; Vega-Mercado , H. Dehytration of Foods ; International Thomson Publishing : New York , 1996 .
   Google Scholar
• Geankoplis , C.J. Transport Processes and Unit Operations, , 3rd Ed ; PTR Prentice Hall : Englewood Cliffs , NJ , 1993 .
   Google Scholar
• Hsu , C.T. ; Cheng , P. A singular perturbation solution for Couette flow over a semi-infinite porous bed . Journal of Fluids Engineering 1991 , 113 , 137 – 142 .
   Web of Science ®Google Scholar
• Bear , J. Dynamics of Fluids in Porous Media ; Dover Publications : New York , 1988 .
   Google Scholar
• Stanish , M.A. ; Schajer , G.S. ; Kayihan , F.A. Mathematical model of drying for hygroscopic porous media . AIChE Journal 1986 , 32 , 1301 – 1311 .
   Web of Science ®Google Scholar
• Ni , H. ; Datta , A.K. ; Tottance , K.E. Moisture transport in intensive microwave heating of biomaterials: A multiphase porous media model . International Journal of Heat and Mass Transfer 1999 , 42 , 1501 – 1512 .
   Web of Science ®Google Scholar
• Wang , Z.H. ; Chen , G. Heat and mass transfer in fixed-bed drying . Chemical Engineering Science 1999 , 54 , 4233 – 4243 .
   Web of Science ®Google Scholar
• Wang , Z.H. ; Chen , G. Heat and mass transfer in batch fluidized drying of porous particles . Chemical Engineering Science 2000 , 55 , 1857 – 1869 .
   Web of Science ®Google Scholar
• Wang , Z.H. ; Chen , G. Theoretical study of fluidized bed drying with microwave heating . Industrial Engineering and Chemistry Research 2000 , 59 , 775 – 782 .
   Google Scholar
• Chen , G. ; Wang , W. ; Mujumdar , A.S. Theoretical study of microwave heating patterns on batch fluidized bed drying of porous material . Chemical Engineering Science 2001 , 56 , 6823 – 6835 .
   Web of Science ®Google Scholar
• Wang , Z.H. ; Shi , M.H. The effects of sublimation-condensation region on heat and mass transfer during microwave freeze drying . Journal of Heat Transfer 1998 , 120 , 654 – 660 .
   Web of Science ®Google Scholar
• Wang , Z.H. ; Shi , M.H. Numerical study on sublimation-condensation phenomena during microwave freeze drying . Chemical Engineering Science 1998 , 53 , 3189 – 3197 .
   Web of Science ®Google Scholar
• Wang , W. ; Chen , G. Numerical investigation on dielectric material assisted microwave freeze-drying of aqueous mannitol solution . Drying Technology 2003 , 21 , 995 – 1017 .
   Web of Science ®Google Scholar
• Millman , M.J. ; Liapis , A.I. ; Marchello , J.M. Analysis of the lyophilization process using a sorption-sublimation model and various operational policies . AIChE Journal 1985 , 31 , 1594 – 1604 .
   Web of Science ®Google Scholar
• Rizvi , S.S.H. Thermodynamic properties of foods in dehydration . In Engineering Properties of Foods, , 2nd Ed ; Rao , M.A. , Rizvi , S.S.H. , Eds.; Marcel Dekker : New York , 1995 .
   Google Scholar
• Meredith , R. Engineers’ Handbook of Industrial Microwave Heating ; The Institution of Electrical Engineers : London , 1998 .
   Google Scholar
• Turner , I. ; Jolly , P. The effect of dielectric properties on microwave drying kinetics . Journal of Microwave Power and Electromagnetic Energy 1990 , 25 , 211 – 223 .
   Web of Science ®Google Scholar
• Jolly , P. ; Turner , I. Non-linear field solutions of one-dimensional microwave heating . Journal of Microwave Power and Electromagnetic Energy 1990 , 25 , 3 – 15 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Jolly , P.G. Combined microwave and convective drying of a porous material . Drying Technology 1991 , 9 , 1209 – 1269 .
   Web of Science ®Google Scholar
• Liu , F. ; Turner , I. ; Bialkowki , M. A finite-difference time-domain simulation of power density distribution in a dielectric loaded microwave cavity . Journal of Microwave Power and Electromagnetic Energy 1994 , 29 , 138 – 148 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Ferguson , W.J. A study of the power-density distribution generated during the combined microwave and convective drying of softwood . Drying Technology 1995 , 13 , 1411 – 1430 .
   Web of Science ®Google Scholar
• Ratanadecho , P. ; Aoki , K. ; Akahori , M. A numerical and experimental study of microwave drying using a rectangular wave guide . Drying Technology 2001 , 19 , 2209 – 2234 .
   Web of Science ®Google Scholar
• Wang , W. ; Chen , G. ; Gao , F. Effect of dielectric material on microwave freeze-drying of skim milk . Drying Technology 2005 , 23 , 317 – 340 .
   Web of Science ®Google Scholar
• Wang , W. ; Chen , G. Theoretical study on microwave freeze-drying of an aqueous pharmaceutical excipient with the aid of dielectric material . Drying Technology 2005 , 23 , 2147 – 2168 .
   Web of Science ®Google Scholar
• Itaya , Y. ; Kobayashi , T. ; Hayakawa , K. Three-dimensional heat and mass transfer with viscoelastic strain-stress formation in composite food during drying . International Journal of Heat and Mass Transfer 1995 , 38 , 1173 – 1185 .
   Web of Science ®Google Scholar
• Hasatani , M. ; Itaya , Y. Drying-induced strain and stress: A review . Drying Technology 1996 , 14 , 1011 – 1040 .
   Web of Science ®Google Scholar
• Itaya , Y. ; Mori , S. ; Hasatani , M. Effect of intermittent heating on drying-induced strain-stress of molded clay . Drying Technology 1999 , 17 , 1261 – 1271 .
   Web of Science ®Google Scholar
• Musielak , G. Influence of the drying medium parameters on drying induced stresses . Drying Technology 2000 , 18 , 561 – 581 .
   Web of Science ®Google Scholar
• Pang , S. Modeling of stress development during drying and relief during steaming in Pinus radiata lumber . Drying Technology 2000 , 18 , 1677 – 1696 .
   Web of Science ®Google Scholar
• Yang , H. ; Sakai , N. ; Watanabe , M. Drying model with non-isotropic shrinkage deformation undergoing simultaneous heat and mass transfer . Drying Technology 2001 , 19 , 1441 – 1460 .
   Web of Science ®Google Scholar
• Perre , P. ; May , B.K. A numerical drying model that accounts for the coupling between transfers and solid mechanics . Case of highly deformable products. Drying Technology 2001 , 19 , 1629 – 1643 .
   Web of Science ®Google Scholar
• Chausi , B. ; Couture , F. ; Roques , M.A. Modelling of multicomponent mass transport in deformable media: Application to dewatering impregnation soaking process . Drying Technology 2001 , 19 , 2081 – 2101 .
   Web of Science ®Google Scholar
• Kowalski , S.J. Thermomechanical approach to shrinking and cracking phenomena in drying . Drying Technology 2001 , 19 , 731 – 765 .
   Web of Science ®Google Scholar
• Kowalski , S.J. Mathematical modelling of shrinkage during drying . Drying Technology 1996 , 14 , 307 – 331 .
   Web of Science ®Google Scholar
• Kowalski , S.J. Drying processes involving permanent deformations of dried materials . International Journal of Engineering Science 1996 , 34 , 1491 – 1506 .
   Web of Science ®Google Scholar
• Banaszak , J. ; Kowalski , S.J. Stresses in viscoelastic plate dried convectively . Drying Technology 1999 , 17 , 97 – 117 .
   Web of Science ®Google Scholar
• Kowalski , S.J. ; Rybicki , A. Drying stress formation by inhomogeneous moisture and temperature distribution . Transport in Porous Media 1996 , 24 , 139 – 156 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Perre , P. Vacuum drying of wood with radiative heating: II . Comparison between theory and experiment. AIChE Journal 2004 , 50 , 108 – 118 .
   Web of Science ®Google Scholar
• Wei , C.K. ; Davis , H.T. ; Davis , E.A. ; Gordon , J. Heat and mass transfer in water-laden sandstone: Convective heating . AIChE Journal 1985 , 31 , 1338 – 1348 .
   Web of Science ®Google Scholar
• Nasrallah , S.B. ; Perre , P. Detailed study of a model of heat and mass transfer during convective drying of porous media . International Journal of Heat and Mass Transfer 1988 , 31 , 957 – 967 .
   Web of Science ®Google Scholar
• Ilic , M. ; Turner , I.W. Convective drying of a consolidated slab of wet porous material . International Journal of Heat and Mass Transfer 1989 , 32 , 2351 – 2362 .
   Web of Science ®Google Scholar
• Chen , P. ; Pei , D.C.T. A mathematical model of drying processes. International Journal of Heat and Mass Transfer 1989, 32, 297–310.
   Web of Science ®Google Scholar
• Constant , T. ; Moyne , C. ; Perre , P. Drying with internal heat generation: Theoretical aspects and application to microwave heating . AIChE Journal 1996 , 42 , 359 – 368 .
   Web of Science ®Google Scholar
• Ni , H. ; Datta , A.K. Heat and moisture transfer in baking of potato slabs . Drying Technology 1999 , 17 , 2069 – 2092 .
   Web of Science ®Google Scholar
• Sutherland , J.W. ; Turner , I.W. ; Northway , R.L. A theoretical and experimental investigation of the convective drying of Australian Pinus-radiata timber . Drying Technology 1994 , 12 , 1815 – 1839 .
   Web of Science ®Google Scholar
• Ferguson , W.J. ; Turner , I.W. A comparison of the finite-element and control-volume numerical-solution techniques applied to timber drying problems below the boiling-point . International Journal for Numerical Methods in Engineering 1995 , 38 , 451 – 467 .
   Web of Science ®Google Scholar
• Ferguson , W.J. ; Turner , I.W. A control volume finite element numerical simulation of the drying of spruce . Journal of Computational Physics 1996 , 125 , 59 – 70 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Perre , P.A. Comparison of the drying simulation codes transpore and wood2d which are used for the modeling of 2-dimensional wood drying processes . Drying Technology 1995 , 13 , 695 – 735 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Perre , P. A synopsis of the strategies and efficient resolution techniques used for modelling and numerically simulating the drying process . In Numerical Methods and Mathematical Modelling of the Drying Process ; Turner , I.W. , Mujumdar , A.S. , Eds.; Marcel Dekker : New York , 1996 .
   Google Scholar
• Turner , I.W. ; Perre , P.A. The use of implicit flux limiting schemes in the simulation of the drying process: A new maximum flow sensor applied to phase mobilities . Applied Mathematical Modelling 2001 , 25 , 513 – 540 .
   Web of Science ®Google Scholar
• Perre , P. ; Turner , I.W. Microwave drying of softwood in an oversized waveguide . AIChE Journal 1997 , 43 , 2579 – 2595 .
   Web of Science ®Google Scholar
• Perre , P. ; Turner , I.W. Transpore: A generic heat and mass transfer computational model for understanding and visualising the drying of porous media . Drying Technology 1999 , 17 , 1273 – 1289 .
   Web of Science ®Google Scholar
• Perre , P. ; Turner , I.W. A 3-D version of transpore: A comprehensive heat and mass transfer computational model for simulating the drying of porous media . International Journal of Heat and Mass Transfer 1999 , 42 , 4501 – 4521 .
   Web of Science ®Google Scholar
• Perre , P. ; Turner , I.W. ; Passard , J. 2-D solution for drying with internal vaporization of anisotropic media . AIChE Journal 1999 , 45 , 13 – 26 .
   Web of Science ®Google Scholar
• Turner , I.W. ; Puiggali , J.R. ; Jomaa , W. A numerical investigation of combined microwave and convective drying of a hygroscopic porous material: A study based on pine wood . Chemical Engineering Research & Design 1998 , 76 , 193 – 209 .
   Web of Science ®Google Scholar
• Wang , W. ; Thorat , B.N. ; Chen , G. ; Mujumdar , A.S. Simulation of fluidized bed drying of carrot with microwave heating . Drying Technology 2002 , 20 , 1855 – 1867 .
   Web of Science ®Google Scholar
• Ma , Y.H. ; Peltre , P.R. Freeze dehydration by microwave energy: Part I . Theoretical investigation. AIChE Journal 1975 , 21 , 335 – 344 .
   Web of Science ®Google Scholar
• Ang , T.K. ; Ford , J.D. ; Pei , D.C.T. Microwave freeze drying of food: A theoretical investigation . International Journal of Heat and Mass Transfer 1977 , 20 , 517 – 526 .
   Web of Science ®Google Scholar
• Lin , S. Exact solution of the sublimation problem in a porous medium . Journal of Heat Transfer-Transactions of the ASME 1981 , 103 , 165 – 168 .
   Web of Science ®Google Scholar
• Lin , S. Exact solution of the desublimation problem in a porous medium . International Journal of Heat and Mass Transfer 1982 , 25 , 625 – 629 .
   Web of Science ®Google Scholar
• Lin , S. Exact solution of the sublimation problem in a porous medium—2 . With an unknown temperature and vapor concentration at the moving sublimation front. Journal of Heat Transfer 1982 , 104 , 808 – 811 .
   Google Scholar
• Fey , Y.C. ; Boles , M.A. Analytical study of the effect of convection heat transfer on the sublimation of a frozen semi-infinite porous medium . International Journal of Heat and Mass Transfer 1987 , 30 , 771 – 779 .
   Web of Science ®Google Scholar
• Fey , Y.C. ; Boles , M.A. Analytical study of the effect of the Darcy and Fick laws on the sublimation of a frozen semi-infinite porous medium . Journal of Heat Transfer 1987 , 109 , 1045 – 1048 .
   Web of Science ®Google Scholar
• Fey , Y.C. ; Boles , M.A. Analytical study of vacuum-sublimation in an initially partially filled frozen porous medium with recondensation . International Journal of Heat and Mass Transfer 1988 , 31 , 1645 – 1653 .
   Web of Science ®Google Scholar
• Fey , Y.C. ; Boles , M.A. Effect of mass convection on vacuum-sublimation in an initially partially filled frozen porous medium . Drying Technology 1988 , 6 , 69 – 94 .
   Web of Science ®Google Scholar
• Fey , Y.C. ; Boles , M.A. Parametric analysis of self-freezing in an initially wet porous medium . International Journal of Heat and Fluid Flow 1988 , 9 , 147 – 155 .
   Web of Science ®Google Scholar
• Litchfield , R.J. ; Liapis , A.I. Adsorption-sublimation model for a freeze dryer . Chemical Engineering Science 1979 , 34 , 1085 – 1090 .
   Web of Science ®Google Scholar
• Liapis , A.I. ; Bruttini , R. Freeze Drying . In Handbook of Industrial Drying, , 2nd Ed , Vol. 1 ; Mujumdar , A.S. , Ed.; Marcel Dekker : New York , 1995 ; 305 – 343 .
   Google Scholar
• Sadikoglu , H. ; Liapis , A.I. Mathematical modeling of the primary and secondary drying stages of bulk solution freeze-drying in trays: Parameter estimation and model discrimination by comparison of theoretical results with experimental data . Drying Technology 1997 , 15 , 791 – 810 .
   Web of Science ®Google Scholar
• Sheehan , P. ; Liapis , A.I. Modeling of the primary and secondary drying stages of the freeze drying of pharmaceutical products in vials: Numerical results obtained from the solution of a dynamic and spatially multi-dimensional lyophilization model for different operational policies . Biotechnology and Bioengineering 1998 , 60 , 712 – 728 .
   PubMed Web of Science ®Google Scholar
• Wang , W. ; Chen , G. Heat and mass transfer in dielectric-material-assisted microwave freeze-drying of skim milk with hygroscopic effect . Chemical Engineering Science 2005 , 60 , 6542 – 6550 .
   Web of Science ®Google Scholar