Hot air and freeze-drying of high-value foods: a review.

A mathematical analysis of affinity membrane bioseparations

Network modeling of the convective flow and diffusion of molecules adsorbing in monoliths and in porous particles packed in a chromatographic column.

The parallel transport of a protein by surface and pore diffusion within a highly porous ion exchanger is studied by measuring equilibria and uptake curves for adsorption of bovine serum albumin (BSA) on two different strongly basic chitosan ion exchangers (hard gels): Ch-2503 and Ch-2507 at pH 6.9 and 298 K. Experimenlal equilibrium isotherms are correlated by the Langmuir equation. Intraparticle effective diffusivities of BSA (D eff ) are determined from the homogeneous Fickian diffusion model, increasing with the bulk phase concentration increase of BSA (Co). It suggests the existence of parallel diffusion. The surface diffusivity D s for the parallel diffusion model is determined from the D eff , and D s =0.47X10 -13 m 2 /s (Ch-2507) and 2.4X10 -13 m 2 /s (Ch-2503) were obtained. Pore diffusivities based on the pore diffusion control (D' p ) are obtained by matching the shrinking core model with the experimental uptake curves. D' p decreases with increasing C 0 . Since D' p in Ch-2507 is constant when c 0 ≥1 kg/m 3 , the constant value 2.7X10 -11 m 2 /s is taken as the accurate pore diffusivity (D p ). As D' p in Ch-2503 does not approach a constant value, D p =1.0X10 -11 m 2 /s is determined by matching the parallel diffusion model with the uptake data, and the model calculated using experimental values of D s and D p agrees reasonably well with the uptake data for Ch-2507 and Ch-2503. This theoretical approach may be applied not only for intraparticle diffusion of proteions but any adsorbates in porous materials

Parallel transport of BSA by surface and pore diffusion in strongly basic chitosan

This paper is focused on the modelling of the primary drying of a lyophilization process in vials. A detailed mono-dimensional model taking into account mass and energy balances in the dried layer and at the sublimating interface, energy balance in the frozen layer and along the vial wall is set up; the mathematical model is validated using experimental data obtained in a pilot scale freeze-dryer, pointing out that the role of the glass wall can be relevant on the dynamics of the process. This model is suitable and has been used for off-line optimization; for on-line monitoring purposes, i.e. observer design, and for model-based control design such a detailed model is not useful, due to the high number of equations and of processes taken into consideration. Thus, two simplified models, that allow for analytical solution, have been developed: both models assume pseudo-stationary conditions because of the slow dynamics of the process, but while the first does not take into consideration the heat balance at the vial wall, this is explicitly considered in the second model. The results obtained with both models have been compared with the predictions of the detailed model for validation purposes.

Development of simplified models for the freeze-drying process and investigation of the optimal operating conditions

The freeze-drying process is studied under various operational policies through the use of a sorption-sublimation model. The operational policy that provides the shortest drying times keeps the pressure at its lowest value. The upper and lower heating plates are independently controlled so that the material constraints are encountered and held throughout the free water removal phase.

Under certain conditions, and for the case of samples of small thickness, the sorbed water profiles may have segments whose bound water concentrations are higher than those at the start of the free water removal phase. It is shown that the criterion used in terminating the freeze-drying process is of extreme importance, since it may lead to an undesirable sorbed water profile which may deteriorate the quality of the dried product.

An analysis of the lyophilization process using a sorption-sublimation model and various operational policies

Modeling and analysis of biospecific adsorption in a finite bath

Guidelines for the desirable operation of batch freeze driers during the removal of free water

Summary

An economic analysis of various operational policies associated with a batch freeze dryer is presented. Skim milk is used as a model material. It is shown that the lowest cost of production corresponds to the highest production rate. This occurs when large sample thicknesses are used, the chamber pressure is at its lowest value and the upper and lower heating plates are independently controlled such that the melting and scorch constraints are both encountered and held during the free water removal phase. Therefore, the operational regime that provides the shortest drying times during the free water removal phase (Millman, Liapis & Marchello, 1984, 1985) will also provide the smallest production costs and highest capacities.

A. I. Liapis

Papers

An analysis of the lyophilization process using a sorption-sublimation model and various operational policies

Modeling and analysis of biospecific adsorption in a finite bath

Guidelines for the desirable operation of batch freeze driers during the removal of free water

Note on the economics of batch freeze dryers