Theoretical Study on Microwave Freeze-Drying of an Aqueous Pharmaceutical Excipient with the Aid of Dielectric Material

Abstract

A mathematic model of simultaneous heat and mass transfer for the dielectric material assisted microwave freeze-drying was derived and solved numerically using the finite-deference technique with two moving boundaries. Lactose, a typical pharmaceutical excipient, was used as the representative solid material in the aqueous solution to be freeze-dried. Silicon carbide (SiC) was selected as the dielectric material. Numerical results show that the dielectric material can significantly enhance the microwave freeze-drying process. Under typical operating conditions, the drying time is 43% shorter than that of ordinary microwave freeze-drying. Temperature variations at sublimation fronts were examined in order to determine the appropriate microwave power input. Profiles of temperature, ice saturation, vapor concentration, and pressure during freeze-drying are presented, and rate-controlling mechanisms are discussed.     

Numerical Investigation on Dielectric Material Assisted Microwave Freeze-Drying of Aqueous Mannitol Solution

The dielectric material assisted microwave freeze-drying was investigated theoretically in this study. A coupled heat and mass transfer model was developed considering distributions of the temperature, ice saturation and vapor mass concentration inside the material being dried, as well as the vapor sublimation-desublimation in the frozen region. The effects of temperature and saturation on the effective conductivities were analyzed based on heat and mass flux equations. The model was solved numerically by the variable time-step finite-deference technique with two movable boundaries in an initially unsaturated porous sphere frozen from an aqueous solution of mannitol. The sintered silicon carbide (SiC) was selected as the dielectric material. The results show that dielectric material can significantly enhance microwave freeze-drying process. For case of the dielectric field strength, E = 4000 V/m under typical operating conditions, the drying time is 2081 s, 30.1% shorter and 47.2% longer, respectively, than those for E = 2000V/m and E = 6000 V/m. The heat and mass transfer mechanisms during the drying process were discussed.     

Numerical Investigation on Dielectric Material Assisted Microwave Freeze-Drying of Aqueous Mannitol Solution

Abstract

The dielectric material assisted microwave freeze-drying was investigated theoretically in this study. A coupled heat and mass transfer model was developed considering distributions of the temperature, ice saturation and vapor mass concentration inside the material being dried, as well as the vapor sublimation-desublimation in the frozen region. The effects of temperature and saturation on the effective conductivities were analyzed based on heat and mass flux equations. The model was solved numerically by the variable time-step finite-deference technique with two movable boundaries in an initially unsaturated porous sphere frozen from an aqueous solution of mannitol. The sintered silicon carbide (SiC) was selected as the dielectric material. The results show that dielectric material can significantly enhance microwave freeze-drying process. For case of the dielectric field strength, E = 4000 V/m under typical operating conditions, the drying time is 2081 s, 30.1% shorter and 47.2% longer, respectively, than those for E = 2000V/m and E = 6000 V/m. The heat and mass transfer mechanisms during the drying process were discussed.     

Analysis of Heat and Mass Transfer in Freeze Drying

The main objective of this work is to build a mathematical model that describes heat and mass transfer in freeze-drying when both plate heating and radiation heating are applied and also to provide further understanding of the mechanism of the drying process. The model, unlike other models, may be used for situations in which sublimation occurs within a temperature range, i.e., the non-existence of a sharp interface and also for cases in which more than one interface may form. The developed model has been tested against experimental measurements of freeze-drying of milk under different operating conditions. Measurements were done using Virtis BT3.3ES freeze dryer with vertical manifolds. The milk was contained in a glassware, specially designed for this project. Four thermocouples were fixed at different positions to track the drying progress. The experimental measurements show no significant shrinkage in the frozen milk when dried, leaving the milk highly porous in structure. In this experimental work, the low thermal conductivity of the dried layer was found to control the process without any significant mass transfer resistance. This includes plate heating where drying was found to progress from the heating surface similar to radiation heating. This is unlike what has been reported in some of literature that drying starts always from the top surface. The model, which was based on heat transfer control, showed a reasonable agreement with the experimental measurements of both plate heating and radiation heating.     

真空冷冻干燥非稳态热质传递模型的应用

真空冷冻干燥非稳态热质传递模型的应用齐锡龄１杜小泽２李惟毅１（１天津大学热能工程系，天津３０００７２）（２清华大学热能工程系，北京１０００８４）关键词冷冻干燥热质传递升华压力１引言通过理论计算确定真空冷冻干燥速率或干燥时间对指导生产实践很有意义。但是...     

介电材料辅助的微波冷冻干燥的数值模拟

通过数值求解一个考虑吸湿效应的带有移动升华界面的多孔介质热、质传递耦合模型,理论考察介电材料对微波加热冷冻干燥过程的影响.介电材料用烧结的碳化硅(SiC).甘露醇,一种典型的药物赋形剂被选为待干溶液中的溶质.模拟结果表明在微波冷冻干燥过程中使用介电材料可以加快冷冻干燥速率,特别是在待干溶液的固含量很低或者固体产品的介电损耗因子很小的情况下尤为有效.模型预测和实验测定的干燥曲线相比较显示了良好的一致性.通过考察冰饱和度和温度的分布侧形,研究分析了物料内部的质热传递机理,并讨论了干燥速率的控制因素.     

介电材料辅助的微波冷冻干燥的实验研究

设计、加工和装配了一套实验室规模的微波冷冻干燥装置,旨在实验验证介电材料对微波冷冻干燥液体物料的强化作用。介电材料用烧结的碳化硅(SiC),石英玻璃作为介电材料的参照物;甘露醇,一种典型的药物赋形剂被选为待干溶液中的溶质。实验结果表明使用介电材料可以有效地强化微波冷冻干燥过程。与传统冷冻干燥相比干燥速率大大加快,在试验条件下干燥时间可以节省20%。微波加热逐渐生效并且主要体现在干燥过程的后半部分。当溶液中的固含量很低或者固体物质具有很小的介电损耗因子时,如果不用介电材料,微波加热的效果不明显。     

具有电介质核心多孔介质微波冷冻干燥过程的耦合传热传质的数值研究

利用变时间步长的有限体积法对具有电介质核心多孔介质微波冷冻干燥的耦合热质传递过程进行了数值模拟。计算结果表明：在有电介质核的多孔介质内部存在着两个升华界面,该双升华界面模型成功地模拟了该干燥过程：合理的选用电介质核心可以大大缩短干燥时间,对于几个大小分别为1．0,1.5,2．0和2．5mm的电介质核,其单位体积所需干燥时间同无核相比分别减少了8％,19％,33％,48％：在相同的电场强度下,电介质核的损耗系数越大,所需干燥时间越短。     

Determination of Optimum Drying Condition of VIP Core Material by Wet Method

Vacuum insulation panel (VIP) core materials were successfully fabricated by wet method. The phase composition, microstructure, and thermal conductivity of VIP core materials were investigated. The density of VIP core materials was 176 kg/m³, while the mean thermal conductivity of VIP core materials was about 31 mW/(m · K). The mean thermal conductivities of VIPs were 2.78 mW/(m · K), 2.62 mW/(m · K), 2.47 mW/(m · K), 2.5 mW/(m · K), and 2.4 mW/(m · K), which correlated to VIP core materials that had been dried at 150°C for 30 min, 60 min, 90 min, and at 170°C for 30 min and 60 min, respectively. However, the mean thermal conductivity evaluated for VIPs with core material that had not been dried was 3.0 mW/(m · K). The thermal conductivity of VIPs with core material that had been dried reached a maximum on the third day and tended to be a steady value with time, whereas the one with core material that had not been dried recorded a high thermal conductivity value and continued to rise in a fluctuating pattern with time. According to the result of the thermogravimetric curve, drying at 150°C for 60 min showed characteristics of complete drying. In addition, the thermal conductivity of VIPs at this drying condition was low and stable. Theoretical and experimental analysis showed that the optimum drying condition for fiberglass VIP core materials was drying at 150°C for 60 min.     

Microwave Freeze Drying of Apple Slices Based on the Dielectric Properties

Freeze drying (FD) yields the best quality of dried apple slices but requires a long drying time and is not cost-effective. To mitigate these problems, a microwave freeze drying (MFD) technique was developed to dry apple slices. The relationship between corona discharge and microwave power at various pressures and initial moisture content conditions was studied to avoid the possibility of corona discharge during MFD. It was found that with change of moisture content and temperature of samples during MFD, the dielectric property also changed, which resulted in dynamic microwave dissipation. Based on the dielectric property of samples, a changed microwave loading scheme can lead to perfect product quality and greatly reduce the drying time; thus, MFD can be used to replace the traditional FD technique.     

Combined Convective and Microwave Drying of Agglomerated Sand: Internal Transfer Modeling with the Gas Pressure Effect

In order to improve the industrial drying (hot air and microwave) of inserts made of agglomerated sand, a comprehensive internal heat and water transfer model has been proposed. In this model, the internal gas phase pressure effect was made perfectly explicit, especially the phenomena of liquid and vapour transfer by filtration and of liquid expulsion at the surface. This model was validated on the basis of the experimental mean water content and core temperature curves for drying trials at different microwave powers. Then, it was used for comparing the drying time and the internal pressure level calculated for four particular processes: a standard process with high temperature air applied all over the time, a strong process with high power microwaves applied all over, and two processes which alternate the two heating modes. It was demonstrated that the combined and alternative processes provide a real possibility for faster drying with less internal pressure and thus with less cracking risk. The microwaves should be applied only in the first hour of the process and with decreasing power. The decrease of the drying time was around 30% with regard to the hot air standard process.     

液体物料冷冻干燥的热点问题

液体物料冷冻干燥广泛应用于制药工业。其过程工艺的重要性正赢得世界范围的研究关注。文献已证实科学方法能够用最少的试差来提高产品质量。过程工艺的建立和规划需要系统地理解冷冻、冷冻干燥、材料科学和质热传递等物理化学过程。本文就液体物料冷冻干燥过程做了简要评述,并对其过程的热点问题做了分析。     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

不粘煤的微波－对流干燥研究

从不粘煤的特性出发，讨论了不粘煤工业干燥的要求；从微波－对流综合干燥传热传质原理分析，论证了这种干燥方式用于不粘煤干燥，在降低温度、控制负荷、提高经济性等方面都有显著成效，并以翔实的试验数据为理论分析作了辅证。     

Pure ice sublimation within vials in a laboratory lyophiliser; comparison of theory with experiment

A two-dimensional axisymmetric, unsteady state model was developed to simulate the coupled heat and mass transfer process that occurs during the sublimation of pure ice from within vials in a laboratory-scale lyophiliser. The theoretical model was solved numerically using an explicit finite difference method. The modified Euler method was used to discretise in time and an adaptive time step strategy was employed to ensure stability. Novel features of the model described here include a consideration of the varying, pressure dependent, insulating effect of the air gap under the curved base of a typical lyophilisation vial and the determination of the effects of radiative heating. The theoretical model was capable of predicting and describing the observed motion of the ice sublimation front, the ice temperature profile, the drying time and the influence of the total pressure. The model also gave a theoretical prediction of the improvement in drying rate that might be achieved by adding an extra energy source. The work provides insights into the understanding of the heat and mass transfer process during the primary drying stage of lyophilisation that can be applied to the optimisation of freeze-drying cycle design.     

The Proper Use of Mass Diffusion Equations in Drying Modeling: Introducing the Drying Intensity Number

This article intends to clearly define the possibilities and limitations offered by a simple diffusion approach of drying. Actually, many works use a simple diffusion equation to model mass transfer during drying, probably because a simple analytical solution of this equation does exist in the case of simple boundary conditions. However, one has to be aware of the limitations of this approach. Using a comprehensive formulation and a relevant computational solution, the most frequent assumptions of the diffusion approach were rigorously tested. It is concluded that analytical solutions must be discarded for several reasons: analytical solutions, either using Dirichlet or third kind boundary conditions, are often misleading and should be avoided; in the drying process, the coupling between heat and mass transfer is mandatory; nonlinearity (variation of diffusivity with moisture content) can hardly be avoided for mass transfer. In order to reach a verdict, a dimensionless number, the Drying Intensity Number (N_DI), is introduced. It allows the level of coupling between heat and mass transfer to be easily assessed. Thanks to this number, a guide is proposed for choosing the right level of modeling, depending on the drying configuration.     

不粘煤的微波－对流干燥研究

从不粘煤的特性出发，讨论了不粘煤工业干燥的要求；从微波－对流综合干燥传热传质原理分析，论证了这种干燥方式用于不粘煤干燥，在降低温度、控制负荷、提高经济性等方面都有显著成效，并以翔实的试验数据为理论分析作了辅证。     

CFD Model of Apple Atmospheric Freeze Drying at Low Temperature

An Internet-controlled atmospheric freeze dryer was designed, built, and tested in the Department of Heat and Mass Transfer, Technical University of ?ód?. A film sublimation-based CFD model was developed and verified using Fluent 6.1 commercial CFD software. The model enables the simulation of phase change and water vapor diffusion process within porous media. Transport of non-condensable species can be calculated with species transport inbuilt model of Fluent 6.1 and used to predict sublimation rate under given conditions. Results were compared with AFD experimental data of 10-mm Idared apple cubes. The viability of applying the film sublimation model to atmospheric freeze-drying process was demonstrated. Higher mass flux was found on the leading edge, relatively uniform mass flux within the porous zone illustrates that vapor diffusion dominates atmospheric freeze drying process at low temperature (below 0°C). CFD results for apple cubes show a predomination of diffusional resistance of porous tissue.     

Experimental Validation of the Heat and Mass Transfer Model for Convective Drying

The aim of this article is to present a self-consistent mathematical model describing the heat and mass transfer phenomena during the convective drying both in the constant and in the falling drying rate periods. This general model is developed on the basis of the theory of mixtures and the thermodynamics of irreversible processes. The boundary conditions are formulated and the numerical algorithm enabling calculation of the temperature and the drying curves in the two mentioned periods of drying is constructed. In this paper much effort is devoted to the experimental validation of the model. The convective drying of a cylindrical sample made of kaolin was examined both experimentally and numerically for comparison and the distribution of temperature and the drying curves were determined. A very good agreement of the experimental and theoretical results is stated.