Optimal control of a freeze dryer—I Theoretical development and quasi steady state analysis

Liapis, Athanasios I.; Litchfield, R.J.

doi:10.1016/0009-2509(79)85009-5

Cited by 81 publications

(47 citation statements)

References 8 publications

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“…Several mathematical equations describing mass and energy transfer have been developed for modeling the freeze-drying process [9][10][11]. Such models account for the removal of frozen water only (sublimation model) or the removal of frozen and bound water (sorption sublimation model), examine the methods of supplying heat and the diffusion mechanisms, describe steady or unsteady state processes, or analyze both transfers under various processing conditions.…”

Section: Introductionmentioning

confidence: 99%

Freeze-Drying Kinetics Approach of Soluble Coffee. Mass Transfer Parameters Estimation

Ghirişan¹,

Drăgan²,

Miclăuş³

2017

Studia UBB Chemia

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ABSTRACT. The present paper presents the freeze-drying kinetics of soluble coffee in order to determine the mass transfer parameters. Several semi-theoretical and empirical models were used to find the best fit to the experimental data. The applied models were compared using the coefficient of determination (R 2 ), the mean relative percent error (P), the root mean square error (RMSE) and the reduced chi-square ( 2 ). The Midilli model was found to fit better to the experimental freeze-drying data comparative to other models. The Fick's second law was employed to determine the effective diffusion coefficient (Deff).

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Section: Introductionmentioning

confidence: 99%

Freeze-Drying Kinetics Approach of Soluble Coffee. Mass Transfer Parameters Estimation

Ghirişan¹,

Drăgan²,

Miclăuş³

2017

Studia UBB Chemia

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“…The model, based on the work of Liapis and Litchfield (1979), consists of an unsteady state energy balance in the dried and frozen regions.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Liapis and Litchfield (1979) presented a model of the freeze-drying of a product in trays where only one surface was exposed to ambient. In this work, two glass covers were placed under and above the sample exposing only the sides of a sample.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…In this work, two glass covers were placed under and above the sample exposing only the sides of a sample. This situation creates the same conditions used in the work of Liapis and Litchfield (1979) with heat and mass flowing in one direction only. In the freezedrying process, a drying layer builds up continuously creating an interface of sublimation -the sublimation front.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Mathematical modeling enhances the understanding of the freeze-drying process and becomes an effective manner of studying its optimization. A computer simulation run on these models is used to analyze drying rates and to predict the surface temperature profile (Liapis, Litchfield, 1979;Millman, Liapis, Marchello, 1985;Pisano, Fissore, Barresi, 2011). Heat and mass transfer models for the freeze-drying process have been developed by a number of researchers and these are presented in scientific literature (Sadikoglu, Liapis, 1997;Sheehan, Liapis, 1998;George, Datta, 2002).…”

Section: Introductionmentioning

confidence: 99%

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Freeze-drying microscopy in mathematical modeling of a biomaterial freeze-drying

Borgognoni

Bevilacqua

Pitombo

2012

Braz. J. Pharm. Sci.

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Transplantation brings hope for many patients. A multidisciplinary approach on this field aims at creating biologically functional tissues to be used as implants and prostheses. The freeze-drying process allows the fundamental properties of these materials to be preserved, making future manipulation and storage easier. Optimizing a freeze-drying cycle is of great importance since it aims at reducing process costs while increasing product quality of this time-and-energy-consuming process. Mathematical modeling comes as a tool to help a better understanding of the process variables behavior and consequently it helps optimization studies. Freeze-drying microscopy is a technique usually applied to determine critical temperatures of liquid formulations. It has been used in this work to determine the sublimation rates of a biological tissue freeze-drying. The sublimation rates were measured from the speed of the moving interface between the dried and the frozen layer under 21.33, 42.66 and 63.99 Pa. The studied variables were used in a theoretical model to simulate various temperature profiles of the freeze-drying process. Good agreement between the experimental and the simulated results was found.Uniterms: Freeze-drying microscopy. Bovine pericardium. Mathematical modeling.A prática da transplantação traz esperança para muitos pacientes. Uma visão multidisciplinar nessa área visa à produção de tecidos biológicos para serem utilizados como implantes e próteses. A liofilização é um processo de secagem que preserva características essenciais desses materiais, facilitando sua manipulação e armazenamento. A liofilização é um processo que requer muito tempo e energia e sua otimização é muito importante, pois permite reduzir custos de processo melhorando a qualidade do produto. A modelagem matemática é uma ferramenta que permite descrever o comportamento do produto durante o processo e, consequentemente, auxilia os estudos de otimização. Microscopia óptica acoplada à liofilização, uma técnica usualmente aplicada na determinação de temperaturas críticas de formulações líquidas, foi utilizada neste trabalho na determinação de taxas de sublimação da liofilização de um tecido biológico. As taxas de sublimação foram calculadas a partir da velocidade da interface entre a camada seca e congelada, sob pressões de 21,33, 42,66 e 63,99 Pa. As variáveis estudadas foram usadas em um modelo matemático teórico, que simula os perfis de temperatura do produto durante o ciclo de liofilização. Os resultados apresentados demonstraram boa relação entre os dados experimentais e simulados.Unitermos: Microscopia óptica acoplada à liofilização. Pericárdio bovino. Modelagem matemática.

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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

Sheehan

Liapis

1998

Biotechnol. Bioeng.

141

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A rigorous unsteady state and spatially multidimensional model is presented and solved to describe the dynamic behavior of the primary and secondary drying stages of the lyophilization of a pharmaceutical product in vials for different operational policies. The results in this work strongly motivate the aggressive control of freeze drying and it is found that heat input control that runs the process close to the melting and scorch temperature constraints yields (i) faster drying times, and (ii) more uniform distributions of temperature and concentration of bound water at the end of the secondary drying stage.

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Optimal control of a freeze dryer—I Theoretical development and quasi steady state analysis

Cited by 81 publications

References 8 publications

Freeze-Drying Kinetics Approach of Soluble Coffee. Mass Transfer Parameters Estimation

Freeze-Drying Kinetics Approach of Soluble Coffee. Mass Transfer Parameters Estimation

Freeze-drying microscopy in mathematical modeling of a biomaterial freeze-drying

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

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