Food drying at sub-zero temperature: Importance of glassy phase on product quality
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Published:
Nov 16, 2018
Keywords:
food drying glass transition vacuum freeze-drying atmospheric freeze-drying
Main Article Content
Abstract
Large number of drying researches have been carried out in pharmaceutical and food sectors with particular interest of the quality assurance. Freeze-drying is known as one of the best drying method for maintaining original product qualities. However, it involves numbers of potential factors that lead quality loss of the product. This review elucidated the mechanisms of freeze-drying with particular focus on the phenomena relating to the glassy phase. Freezing process involves formation of the ice crystal and freeze-concentrated phase (i.e. glassy phase), and the relaxation of the glassy phase. This process determines ice crystal morphology, the degree of freeze-concentration and the crystallinity of the concentrated matters. Product temperature during freeze-drying affects various quality attributes, and the influence was dependent on how high is the temperature from the glass transition temperature. These explanations were made with the X-ray CT images of freeze-dried materials. It is important to understand the mechanisms of phenomena in the glassy phase in order to optimize product quality. A method that can deal with the complicated interaction of the kinetics in a glassy matter could be a clue.
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Nakagawa, K. (2018). Food drying at sub-zero temperature: Importance of glassy phase on product quality. Science, Engineering and Health Studies, 12(3), 125–137. https://doi.org/10.14456/sehs.2018.12
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Review Articles
References
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Ablett, S., Izzard, M. J., Lillford, P. J. (1992). Differential scanning calorimetric study of frozen sucrose and glycerol solutions. Journal of the Chemical Society, Faraday Transactions, 88(6), 789-794.
Alves-Filho, O. (2002). Combined innovative heat pump drying technologies and new cold extrusion techniques for production of instant foods. Drying Technology, 20(8), 1541-1557.
Andrieu, J., Vessot, S. (2018). A review on experimental determination and optimization of physical quality factors during pharmaceuticals freeze-drying cycles. Drying Technology, 36(2), 129-145.
Banga, J. R., Balsa-Canto, E., Moles, C. G., Alonso, A. A. (2003). Improving food processing using modern optimization methods. Trends in Food Science & Technology, 14(4), 131-144.
Banga, J. R., Paul Singh, R. (1994). Optimization of air drying of foods. Journal of Food Engineering, 23(2), 189-211.
Baş, D., Boyacı, İ. H. (2007). Modeling and optimization I: Usability of response surface methodology. Journal of Food Engineering, 78(3), 836-845.
Carpenter, J. F., Pikal, M. J., Chang, B. S., Randolph, T. W. (1997). Rational design of stable lyophilized protein formulations: some practical advice. Pharmaceutical Research, 14(8), 969-975.
Chou, S. K., Chua, K. J. (2001). New hybrid drying technologies for heat sensitive foodstuffs. Trends in Food Science & Technology, 12(10), 359-369.
Ciurzyńska, A., Lenart, A. (2011). Freeze-drying-application in food processing and biotechnology: A review. Polish Journal of Food and Nutrition Sciences, 61(3), 165-171.
Claussen, I. C., Andresen, T., Eikevik, T. M., Str⊘mmen, I. (2007a). Atmospheric freeze drying-modeling and simulation of a tunnel dryer. Drying Technology, 25(12), 1959-1965.
Claussen, I. C., Ustad, T. S., Str⊘mmen, I., Walde, P. M. (2007b). Atmospheric freeze drying: A review. Drying Technology, 25(6), 947-957.
Cogdill, R. P., Drennen, J. K. (2008). Risk-based quality by design (QbD): A taguchi perspective on the assessment of product quality, and the quantitative linkage of drug product parameters and clinical performance. Journal of Pharmaceutical Innovation, 3(1), 23-29.
Devahastin, S., Niamnuy, C. (2010). Modelling quality changes of fruits and vegetables during drying: A review. International Journal of Food Science & Technology, 45(9), 1755-1767.
Duan, X., Yang, X., Ren, G., Pang, Y., Liu, L., Liu, Y. (2015). Technical aspects in freeze drying of foods. Drying Technology, 34(11), 1271-1285.
Dufour, P. (2006). Control engineering in drying technology: Review and trends. Drying Technology, 24(7), 889-904.
Goshima, H., Forney-Stevens, K. M., Liu, M., Qian, K. K., Tyagi, M., Cicerone, M. T., Pikal, M. J. (2016). Addition of monovalent electrolytes to improve storage stability of freeze-dried protein formulations. Journal of Pharmaceutical Sciences, 105(2), 530-541.
Hubbell, J. H. (1999). Review of photon interaction cross section data in the medical and biological context. Physics in Medicine & Biology, 44(1), R1.
Jangam, S. V. (2011). An overview of recent developments and some R&D challenges related to drying of foods. Drying Technology, 29(12), 1343-1357.
Jangam, S. V., Mujumdar, A. S. (2011). Heat pump assisted drying technology–overview with focus on energy, environment and product quality. Modern drying technology, 121-162.
Kasper, J. C., Friess, W. (2011). The freezing step in lyophilization: physico-chemical fundamentals, freezing methods and consequences on process performance and quality attributes of biopharmaceuticals. European Journal of Pharmaceutics and Biopharmaceutics, 78(2), 248-263.
Kawai, K., Suzuki, T., Oguni, M. (2006). Low-temperature glass transitions of quenched and annealed bovine serum albumin aqueous solutions. Biophysical Journal, 90(10), 3732-3738.
Kinahan, P. E., Hasegawa, B. H., Beyer, T. (2003). X-ray-based attenuation correction for positron emission tomography/computed tomography scanners. Seminars in Nuclear Medicine, 33(3), 166-179.
Kumagai, H., Mizuno, A., Kumagai, H., Yano, T. (1997a). Analysis of water sorption isotherms of superabsorbent polymers by solution thermodynamics. Bioscience, Biotechnology, and Biochemistry, 61(6), 936-941.
Kumagai, H., Seto, H., Sakurai, H., Ishii, K., Kumagai, H. (1997b). Analysis of water sorption behavior of native and denatured proteins by solution thermodynamics. Bioscience, Biotechnology, and Biochemistry, 61(8), 1307-1311.
Kurz, W., Fisher, D. J. (1986). Fundamentals of Solidification. Trans Tech Publications Aedermannsdorf, Switzerland.
Labuza, T. P. (1970). Properties of water as related to the keeping quality of foods, Proceedings 3rd International Conference Food Science and Technology, SOS70. Institute Food Technologists, Washington, DC, p. 618.
Levi, G., Karel, M. (1995). Volumetric shrinkage (collapse) in freeze-dried carbohydrates above their glass transition temperature. Food Research International, 28(2), 145-151.
Levine, H., Slade, L. (1988). Principles of “cryostabilization” technology from structure/ property relationships of carbohydrate/water systems-a review. Cryo-letters, 9(1), 21-63.
Meister, E., Gieseler, H. (2009). Freeze-dry microscopy of protein/sugar mixtures: Drying behavior, interpretation of collapse temperatures and a comparison to corresponding glass transition Data. Journal of Pharmaceutical Sciences, 98(9), 3072-3087.
Midgley, S. M. (2004). A parameterization scheme for the x-ray linear attenuation coefficient and energy absorption coefficient. Physics in Medicine & Biology, 49(2), 307.
Milton, N., Nail, S. L., Akers, M. J. (1997). The crystallization kinetics of glycine hydrochloride from 'frozen' solution. Cryo-letters, 18(6), 335-342.
N'Diaye, M., Degeratu, C., Bouler, J.-M., Chappard, D. (2013). Biomaterial porosity determined by fractal dimensions, succolarity and lacunarity on microcomputed tomographic images. Materials Science and Engineering: C, 33(4), 2025-2030.
Nakagawa, K. (2011). Foam Materials Made from Carbon Nanotubes. In Carbon Nanotubes (Bianco, S., ed.), IntechOpen, DOI: 10.5772/18442. Available from: https://www.intechopen.com/ books/carbon-nanotubes-from-research-to-applications/foam-materials-made-from carbon-nanotubes
Nakagawa, K., Hottot, A., Vessot, S., Andrieu, J. (2006). Influence of controlled nucleation by ultrasounds on ice morphology of frozen formulations for pharmaceutical proteins freeze-drying. Chemical Engineering and Processing: Process Intensification, 45(9), 783-791.
Nakagawa, K., Hottot, A., Vessot, S., Andrieu, J. (2007). Modeling of freezing step during freeze-drying of drugs in vials. AIChE Journal, 53(5), 1362-1372.
Nakagawa, K., Jarunglumlert, T., Adachi, S. (2016a). Structural changes in casein aggregates under frozen conditions affect the entrapment of hydrophobic materials and the digestibility of aggregates. Chemical Engineering Science, 143, 287-296.
Nakagawa, K., Murakami, W., Andrieu, J., Vessot, S. (2009). Freezing step controls the mannitol phase composition heterogeneity. Chemical Engineering Research and Design, 87(8), 1017-1027.
Nakagawa, K., Ritcharoen, W., Sri-Uam, P., Pavasant, P., Adachi, S. (2016b). Antioxidant properties of convective-air-dried Spirulina maxima: Evaluation of phycocyanin retention by a simple mathematical model of air-drying. Food and Bioproducts Processing, 100, 292-302.
Nakagawa, K., Tamiya, S., Do, G., Kono, S., Ochiai, T. (2018a). Observation of glassy state relaxation during annealing of frozen sugar solutions by X-ray computed tomography. European Journal of Pharmaceutics and Biopharmaceutics, 127, 279-287.
Nakagawa, K., Tamiya, S., Sakamoto, S., Do, G., Kono, S. (2018b). Observation of microstructure formation during freeze-drying of dextrin solution by in-situ X-ray computed tomography. Frontiers in Chemistry, 6(418).
Ndiaye, M., Terranova, L., Mallet, R., Mabilleau, G., Chappard, D. (2015). Three-dimensional arrangement of β-tricalcium phosphate granules evaluated by microcomputed tomography and fractal analysis. Acta Biomaterialia, 11(Supplement C), 404-411.
Ohkuma, C., Kawai, K., Viriyarattanasak, C., Mahawanich, T., Tantratian, S., Takai, R., Suzuki, T. (2008). Glass transition properties of frozen and freeze-dried surimi products: Effects of sugar and moisture on the glass transition temperature. Food Hydrocolloids, 22(2), 255-262.
Pikal, M. J. (2004). Mechanisms of protein stabilization during freeze-drying and storage: The relative importance of thermodynamic stabilization and glassy state relaxation dynamics, Freeze-drying/lyophilization of pharmaceutical and biological products. Marcel Dekker, New York, pp. 63-107.
Pikal, M. J., Shah, S. (1990). The collapse temperature in freeze drying: Dependence on measurement methodology and rate of water removal from the glassy phase. International Journal of Pharmaceutics, 62(2), 165-186.
Ratke, L., Voorhees, P. W. (2013). Growth and coarsening: Ostwald ripening in material processing. Springer Science & Business Media.
Ratti, C., (2001). Hot air and freeze-drying of high-value foods: a review. Journal of Food Engineering, 49(4), 311-319.
Sagar, V., Kumar, P. S. (2010). Recent advances in drying and dehydration of fruits and vegetables: a review. Journal of food science and Technology,
47(1), 15-26.
Sahagian, M. E., Goff, H. D. (1994). Effect of freezing rate on the thermal, mechanical and physical aging properties of the glassy state in frozen sucrose solutions. Thermochimica Acta, 246(2), 271-283.
Schladitz, K. (2011). Quantitative micro‐CT. Journal of microscopy, 243(2), 111-117.
Searles, J. A., Carpenter, J. F., Randolph, T. W. (2001a). Annealing to optimize the primary drying rate, reduce freezing-induced drying rate heterogeneity, and determine T′g in pharmaceutical lyophilization. Journal of Pharmaceutical Sciences, 90(7), 872-887.
Searles, J.A., Carpenter, J.F., Randolph, T.W. (2001b). The ice nucleation temperature determines the primary drying rate of lyophilization for samples frozen on a temperature-controlled shelf. Journal of Pharmaceutical Sciences, 90(7), 860-871.
Slade, L., Levine, H., Ievolella, J., Wang, M. (1993). The glassy state phenomenon in applications for the food industry: Application of the food polymer science approach to structure–function relationships of sucrose in cookie and cracker systems. Journal of the Science of Food and Agriculture, 63(2), 133-176.
Slade, L., Levine, H., Reid, D. S. (1991). Beyond water activity: Recent advances based on an alternative approach to the assessment of food quality and safety. Critical Reviews in Food Science and Nutrition, 30(2-3), 115-360.
To, E. C., Flink, J. M. (1978). ‘Collapse’, a structural transition in freeze dried carbohydrates. International Journal of Food Science & Technology, 13(6), 583-594.
Trienekens, J., Zuurbier, P. (2008). Quality and safety standards in the food industry, developments and challenges. International Journal of Production Economics, 113(1), 107-122.
Van den Berg, C. (1986). Water activity. In Concentration and Drying of Foods (MacCarthy, D. ed.), Elsevier Applied Science, London, p. 11.
Wolff, E., Gibert, H. (1990). Atmospheric freeze-drying part 2: Modelling drying kinetics using adsorption isotherms. Drying Technology, 8(2), 405-428.
Yu, L. X. (2008). Pharmaceutical quality by design: product and process development, understanding, and control. Pharmaceutical Research, 25(4), 781-791.
Ablett, S., Izzard, M. J., Lillford, P. J. (1992). Differential scanning calorimetric study of frozen sucrose and glycerol solutions. Journal of the Chemical Society, Faraday Transactions, 88(6), 789-794.
Alves-Filho, O. (2002). Combined innovative heat pump drying technologies and new cold extrusion techniques for production of instant foods. Drying Technology, 20(8), 1541-1557.
Andrieu, J., Vessot, S. (2018). A review on experimental determination and optimization of physical quality factors during pharmaceuticals freeze-drying cycles. Drying Technology, 36(2), 129-145.
Banga, J. R., Balsa-Canto, E., Moles, C. G., Alonso, A. A. (2003). Improving food processing using modern optimization methods. Trends in Food Science & Technology, 14(4), 131-144.
Banga, J. R., Paul Singh, R. (1994). Optimization of air drying of foods. Journal of Food Engineering, 23(2), 189-211.
Baş, D., Boyacı, İ. H. (2007). Modeling and optimization I: Usability of response surface methodology. Journal of Food Engineering, 78(3), 836-845.
Carpenter, J. F., Pikal, M. J., Chang, B. S., Randolph, T. W. (1997). Rational design of stable lyophilized protein formulations: some practical advice. Pharmaceutical Research, 14(8), 969-975.
Chou, S. K., Chua, K. J. (2001). New hybrid drying technologies for heat sensitive foodstuffs. Trends in Food Science & Technology, 12(10), 359-369.
Ciurzyńska, A., Lenart, A. (2011). Freeze-drying-application in food processing and biotechnology: A review. Polish Journal of Food and Nutrition Sciences, 61(3), 165-171.
Claussen, I. C., Andresen, T., Eikevik, T. M., Str⊘mmen, I. (2007a). Atmospheric freeze drying-modeling and simulation of a tunnel dryer. Drying Technology, 25(12), 1959-1965.
Claussen, I. C., Ustad, T. S., Str⊘mmen, I., Walde, P. M. (2007b). Atmospheric freeze drying: A review. Drying Technology, 25(6), 947-957.
Cogdill, R. P., Drennen, J. K. (2008). Risk-based quality by design (QbD): A taguchi perspective on the assessment of product quality, and the quantitative linkage of drug product parameters and clinical performance. Journal of Pharmaceutical Innovation, 3(1), 23-29.
Devahastin, S., Niamnuy, C. (2010). Modelling quality changes of fruits and vegetables during drying: A review. International Journal of Food Science & Technology, 45(9), 1755-1767.
Duan, X., Yang, X., Ren, G., Pang, Y., Liu, L., Liu, Y. (2015). Technical aspects in freeze drying of foods. Drying Technology, 34(11), 1271-1285.
Dufour, P. (2006). Control engineering in drying technology: Review and trends. Drying Technology, 24(7), 889-904.
Goshima, H., Forney-Stevens, K. M., Liu, M., Qian, K. K., Tyagi, M., Cicerone, M. T., Pikal, M. J. (2016). Addition of monovalent electrolytes to improve storage stability of freeze-dried protein formulations. Journal of Pharmaceutical Sciences, 105(2), 530-541.
Hubbell, J. H. (1999). Review of photon interaction cross section data in the medical and biological context. Physics in Medicine & Biology, 44(1), R1.
Jangam, S. V. (2011). An overview of recent developments and some R&D challenges related to drying of foods. Drying Technology, 29(12), 1343-1357.
Jangam, S. V., Mujumdar, A. S. (2011). Heat pump assisted drying technology–overview with focus on energy, environment and product quality. Modern drying technology, 121-162.
Kasper, J. C., Friess, W. (2011). The freezing step in lyophilization: physico-chemical fundamentals, freezing methods and consequences on process performance and quality attributes of biopharmaceuticals. European Journal of Pharmaceutics and Biopharmaceutics, 78(2), 248-263.
Kawai, K., Suzuki, T., Oguni, M. (2006). Low-temperature glass transitions of quenched and annealed bovine serum albumin aqueous solutions. Biophysical Journal, 90(10), 3732-3738.
Kinahan, P. E., Hasegawa, B. H., Beyer, T. (2003). X-ray-based attenuation correction for positron emission tomography/computed tomography scanners. Seminars in Nuclear Medicine, 33(3), 166-179.
Kumagai, H., Mizuno, A., Kumagai, H., Yano, T. (1997a). Analysis of water sorption isotherms of superabsorbent polymers by solution thermodynamics. Bioscience, Biotechnology, and Biochemistry, 61(6), 936-941.
Kumagai, H., Seto, H., Sakurai, H., Ishii, K., Kumagai, H. (1997b). Analysis of water sorption behavior of native and denatured proteins by solution thermodynamics. Bioscience, Biotechnology, and Biochemistry, 61(8), 1307-1311.
Kurz, W., Fisher, D. J. (1986). Fundamentals of Solidification. Trans Tech Publications Aedermannsdorf, Switzerland.
Labuza, T. P. (1970). Properties of water as related to the keeping quality of foods, Proceedings 3rd International Conference Food Science and Technology, SOS70. Institute Food Technologists, Washington, DC, p. 618.
Levi, G., Karel, M. (1995). Volumetric shrinkage (collapse) in freeze-dried carbohydrates above their glass transition temperature. Food Research International, 28(2), 145-151.
Levine, H., Slade, L. (1988). Principles of “cryostabilization” technology from structure/ property relationships of carbohydrate/water systems-a review. Cryo-letters, 9(1), 21-63.
Meister, E., Gieseler, H. (2009). Freeze-dry microscopy of protein/sugar mixtures: Drying behavior, interpretation of collapse temperatures and a comparison to corresponding glass transition Data. Journal of Pharmaceutical Sciences, 98(9), 3072-3087.
Midgley, S. M. (2004). A parameterization scheme for the x-ray linear attenuation coefficient and energy absorption coefficient. Physics in Medicine & Biology, 49(2), 307.
Milton, N., Nail, S. L., Akers, M. J. (1997). The crystallization kinetics of glycine hydrochloride from 'frozen' solution. Cryo-letters, 18(6), 335-342.
N'Diaye, M., Degeratu, C., Bouler, J.-M., Chappard, D. (2013). Biomaterial porosity determined by fractal dimensions, succolarity and lacunarity on microcomputed tomographic images. Materials Science and Engineering: C, 33(4), 2025-2030.
Nakagawa, K. (2011). Foam Materials Made from Carbon Nanotubes. In Carbon Nanotubes (Bianco, S., ed.), IntechOpen, DOI: 10.5772/18442. Available from: https://www.intechopen.com/ books/carbon-nanotubes-from-research-to-applications/foam-materials-made-from carbon-nanotubes
Nakagawa, K., Hottot, A., Vessot, S., Andrieu, J. (2006). Influence of controlled nucleation by ultrasounds on ice morphology of frozen formulations for pharmaceutical proteins freeze-drying. Chemical Engineering and Processing: Process Intensification, 45(9), 783-791.
Nakagawa, K., Hottot, A., Vessot, S., Andrieu, J. (2007). Modeling of freezing step during freeze-drying of drugs in vials. AIChE Journal, 53(5), 1362-1372.
Nakagawa, K., Jarunglumlert, T., Adachi, S. (2016a). Structural changes in casein aggregates under frozen conditions affect the entrapment of hydrophobic materials and the digestibility of aggregates. Chemical Engineering Science, 143, 287-296.
Nakagawa, K., Murakami, W., Andrieu, J., Vessot, S. (2009). Freezing step controls the mannitol phase composition heterogeneity. Chemical Engineering Research and Design, 87(8), 1017-1027.
Nakagawa, K., Ritcharoen, W., Sri-Uam, P., Pavasant, P., Adachi, S. (2016b). Antioxidant properties of convective-air-dried Spirulina maxima: Evaluation of phycocyanin retention by a simple mathematical model of air-drying. Food and Bioproducts Processing, 100, 292-302.
Nakagawa, K., Tamiya, S., Do, G., Kono, S., Ochiai, T. (2018a). Observation of glassy state relaxation during annealing of frozen sugar solutions by X-ray computed tomography. European Journal of Pharmaceutics and Biopharmaceutics, 127, 279-287.
Nakagawa, K., Tamiya, S., Sakamoto, S., Do, G., Kono, S. (2018b). Observation of microstructure formation during freeze-drying of dextrin solution by in-situ X-ray computed tomography. Frontiers in Chemistry, 6(418).
Ndiaye, M., Terranova, L., Mallet, R., Mabilleau, G., Chappard, D. (2015). Three-dimensional arrangement of β-tricalcium phosphate granules evaluated by microcomputed tomography and fractal analysis. Acta Biomaterialia, 11(Supplement C), 404-411.
Ohkuma, C., Kawai, K., Viriyarattanasak, C., Mahawanich, T., Tantratian, S., Takai, R., Suzuki, T. (2008). Glass transition properties of frozen and freeze-dried surimi products: Effects of sugar and moisture on the glass transition temperature. Food Hydrocolloids, 22(2), 255-262.
Pikal, M. J. (2004). Mechanisms of protein stabilization during freeze-drying and storage: The relative importance of thermodynamic stabilization and glassy state relaxation dynamics, Freeze-drying/lyophilization of pharmaceutical and biological products. Marcel Dekker, New York, pp. 63-107.
Pikal, M. J., Shah, S. (1990). The collapse temperature in freeze drying: Dependence on measurement methodology and rate of water removal from the glassy phase. International Journal of Pharmaceutics, 62(2), 165-186.
Ratke, L., Voorhees, P. W. (2013). Growth and coarsening: Ostwald ripening in material processing. Springer Science & Business Media.
Ratti, C., (2001). Hot air and freeze-drying of high-value foods: a review. Journal of Food Engineering, 49(4), 311-319.
Sagar, V., Kumar, P. S. (2010). Recent advances in drying and dehydration of fruits and vegetables: a review. Journal of food science and Technology,
47(1), 15-26.
Sahagian, M. E., Goff, H. D. (1994). Effect of freezing rate on the thermal, mechanical and physical aging properties of the glassy state in frozen sucrose solutions. Thermochimica Acta, 246(2), 271-283.
Schladitz, K. (2011). Quantitative micro‐CT. Journal of microscopy, 243(2), 111-117.
Searles, J. A., Carpenter, J. F., Randolph, T. W. (2001a). Annealing to optimize the primary drying rate, reduce freezing-induced drying rate heterogeneity, and determine T′g in pharmaceutical lyophilization. Journal of Pharmaceutical Sciences, 90(7), 872-887.
Searles, J.A., Carpenter, J.F., Randolph, T.W. (2001b). The ice nucleation temperature determines the primary drying rate of lyophilization for samples frozen on a temperature-controlled shelf. Journal of Pharmaceutical Sciences, 90(7), 860-871.
Slade, L., Levine, H., Ievolella, J., Wang, M. (1993). The glassy state phenomenon in applications for the food industry: Application of the food polymer science approach to structure–function relationships of sucrose in cookie and cracker systems. Journal of the Science of Food and Agriculture, 63(2), 133-176.
Slade, L., Levine, H., Reid, D. S. (1991). Beyond water activity: Recent advances based on an alternative approach to the assessment of food quality and safety. Critical Reviews in Food Science and Nutrition, 30(2-3), 115-360.
To, E. C., Flink, J. M. (1978). ‘Collapse’, a structural transition in freeze dried carbohydrates. International Journal of Food Science & Technology, 13(6), 583-594.
Trienekens, J., Zuurbier, P. (2008). Quality and safety standards in the food industry, developments and challenges. International Journal of Production Economics, 113(1), 107-122.
Van den Berg, C. (1986). Water activity. In Concentration and Drying of Foods (MacCarthy, D. ed.), Elsevier Applied Science, London, p. 11.
Wolff, E., Gibert, H. (1990). Atmospheric freeze-drying part 2: Modelling drying kinetics using adsorption isotherms. Drying Technology, 8(2), 405-428.
Yu, L. X. (2008). Pharmaceutical quality by design: product and process development, understanding, and control. Pharmaceutical Research, 25(4), 781-791.