An Efficient Calculation of Multidimensional Freeze-Drying Problems Using Fixed Grid Method

REFERENCES

• Millman , M.J. ; Liapis , A.I. ; Marchello , J.M. An analysis of the lyophilization process using a sorption-sublimation model and various operation policies . AIChE J 1985 , 31 , 1594 – 1604 [CSA]
   Web of Science ®Google Scholar
• Liapis , A.I. Freeze-drying . In Handbook of Industrial Drying ; Mujumdar , A.S. , Ed.; Marcel Dekker, Inc. : New York , 1987 ; 295 – 326 .
   Google Scholar
• Ratti , C. Hot air and freeze-drying of high-value foods: A review . J. Food Eng. 2001 , 49 , 311 – 319 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Liapis , A.I. ; Litchfield , R.J. Optimal control of a freeze dryer . Chem. Eng. Sci. 1979 , 34 , 975 – 981 [CSA] [CROSSREF]
   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 operation policies . Biotechnol. Bioeng. 1998 , 60 , 712 – 728 [CSA] [CROSSREF]
   PubMed Web of Science ®Google Scholar
• Sadikoglu , H. ; Liapis , A.I. ; Crosser , O.K. Optimal control of the primary and secondary drying stages of bulk solution freeze-drying in trays . Drying Technology 1998 , 16 , 399 – 431 [CSA]
   Web of Science ®Google Scholar
• Sadikoglu , H. ; Ozdemir , M. ; Seker , M. Optimal control of the primary drying stage of freeze-drying of solutions in vials using variational calculus . Drying Technology 2003 , 21 , 1307 – 1331 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Wang , Z.H. ; Shi , M.H. Numerical study on sublimation-condensation phenomena during microwave freeze-drying . Chem. Eng. Sci. 1998 , 53 , 3189 – 3197 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Wang , Z.H. ; Shi , M.H. The effect of sublimation-condensation region on heat and mass transfer during microwave freeze-drying . J. Heat Transfer 1998 , 120 , 654 – 660 [CSA]
   Web of Science ®Google Scholar
• Wu , H. ; Tao , Z. ; Chen , G. ; Deng , H. ; Xu , G. ; Ding , S. Conjugate heat and mass transfer process within porous media with dielectric cores in microwave freeze-drying . Chem. Eng. Sci. 2004 , 59 , 2921 – 2928 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Voller V. ; Cross , M. Accurate solutions of moving boundary problems using the enthalpy method . Int. J. Heat Mass Transfer 1981 , 24 , 545 – 556 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Hirt , C.W. ; Nichols , B.D. Volume of fluid (VOF) method for the dynamics of free boundaries . J. Comp. Physics 1981 , 39 , 205 – 225 [CSA]
   Google Scholar
• 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 . Separ. Technol. 1994 , 4 , 144 – 155 [CSA] [CROSSREF]
   Web of Science ®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 Technol. 1997 , 15 , 791 – 810 [CSA]
   Web of Science ®Google Scholar
• Ferguson , W.J. ; Lewis , R.W. A finite element analysis of freeze-drying of a coffee sample . Comp. Meth. Appl. Mech. Eng. 1993 , 108 , 341 – 352 [CSA] [CROSSREF]
   Google Scholar
• Mascarenhas , W.J. ; Akay , H.U. ; Pikal , M.J. A computational model for finite element analysis of the freeze-drying process. Comp. Meth. Appl. Mech. Eng. 1998, 148, 105–124 [CSA] [CROSSREF]
   Google Scholar
• Song , C.S. ; Nam , J.H. ; Kim , C.-J. ; Ro , S.T. A finite volume analysis of vacuum freeze-drying processes of skim milk solution in trays and vials . Drying Technology 2002 , 20 , 283 – 305 [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Sadikoglu , H. ; Liapis , A.I. ; Crosser , O.K. ; Bruttini , R. Estimation of the effect of product shrinkage on the drying times, heat input and condenser load of the primary and secondary drying stages of the lyophilization process in vials . Drying Technology 1999 , 17 , 2013 – 2035 [CSA]
   Web of Science ®Google Scholar
• Evans , R.B. ; Watson , G.M. ; Mason , E.A. Gaseous diffusion in porous media . J. Chem. Phys. 1962 , 36 , 1894 – 1902 [CSA] [CROSSREF]
   Google Scholar