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.     

Heat and mass transfer model of dielectric-material-assisted microwave freeze-drying of skim milk with hygroscopic effect

A new porous media mathematical model for freeze-drying was developed based on the adsorption-desorption relationship proposed in this paper. A finite difference solution was obtained from a moving boundary problem for the dielectric-material-assisted microwave freeze-drying process. Silicon carbide (SiC) was selected as the dielectric material; and frozen skim milk was used as the aqueous solution to be dried. Simulation results showed that the dielectric material can significantly enhance the microwave freeze-drying process. The drying time was 33.1% shorter than that of ordinary microwave freeze-drying under typical operating conditions. When the solid content of the solution to be freeze-dried was very low, or the solid product had a very small loss factor, microwave heating was less effective without the assistance of dielectric material. The mechanisms of heat and mass transfer during drying were analyzed based on profiles of ice saturation, temperature and vapor concentration. Drying rate-controlling factors were discussed. A comparison was made between the model predictions and the reported experimental data.     

吸湿多孔介质冷冻干燥传质传热模型

本研究在作者提出的吸附—解吸平衡关系的基础上,建立了一个全新的考虑吸湿效应的多孔介质冷冻干燥数学模型。模型用有限差分法进行求解,并带有一个移动边界,以模拟介电材料辅助的微波冷冻干燥过程。介电材料选用碳化硅（SiC）,原料液为脱脂奶。模拟结果表明：介电材料能够有效强化微波冷冻干燥过程。在典型操作条件下,介电材料辅助的微波冷冻干燥所用的时间比普通微波冷冻干燥减少33.1%。当料液中固体含量较低或者固体产品的损耗因子较小时,介电材料对微波加热的效果不明显。基于冰饱和度、温度和水蒸气浓度的分布,本文分析了干燥过程中的传质传热机理,并对干燥速率控制因素进行了讨论。     

Effect of Dielectric Material on Microwave Freeze Drying of Skim Milk

Abstract:

A simultaneous heat and mass transfer model of the dielectric material–assisted microwave freeze drying was derived in this study considering the vapor sublimation-desublimation in the frozen region. The mathematical model was solved numerically by using the finite-difference technique with two moving boundaries. Silicon carbide (SiC) was selected as the dielectric material, and the skim milk was used as the representative solid material in the aqueous solution to be freeze-dried. The results show that the dielectric material can significantly enhance the microwave freeze drying process. The drying time is greatly reduced compared to cases without the aid of the dielectric material. Profiles of the temperature, ice saturation, vapor concentration, and pressure during freeze drying were presented. Mechanisms of the heat and mass transfer inside the material sphere were analyzed. For an initially unsaturated frozen sample of 16 mm in diameter with a 4-mm-diameter dielectric material core, the drying time is 288.2 min, much shorter than 380.1 min of ordinary microwave freeze drying and 455.0 min of conventional vacuum freeze drying, respectively, under typical operating conditions.     

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.     

具有预制孔隙的维生素C水溶液微波冷冻干燥

设计和组装了一套实验室规模的多功能微波冷冻干燥装置，探究了具有初始孔隙的非饱和物料微波冷冻干燥过程。以维生素C为溶质，采用“软冰”冷冻技术制备了初始饱和与非饱和的冷冻样品。结果表明，软冰冷冻制备的样品能够避免崩塌。在35℃和20 Pa条件下，初始非饱和物料的干燥时间比饱和物料缩短了30.4%。SEM表征显示，非饱和物料具有疏松的球状孔隙结构、连通性好，有利于水蒸气的迁移。采用吸波材料碳化硅辅助的微波加热能够进一步强化冷冻干燥过程。在相同条件下，非饱和物料的微波冷冻干燥(5 W功率)时间比常规冷冻干燥(0 W功率)缩短了28.1%，比饱和物料的常规冷冻干燥缩短了50.0%。吸波材料辅助的初始非饱和物料微波冷冻干燥实现了传热传质的同时强化。     

SIMULATION OF FLUIDIZED-BED DRYING OF CARROT WITH MICROWAVE HEATING

A mathematical model of coupled heat and mass transfer was applied to batch fluidized-bed drying with microwave heating of a heat sensitive material—carrot. Four kinds of microwave heating with intermittent variation were examined. The numerical results show that different microwave heating patterns can affect the fluidized bed drying significantly. Changing the microwave input pattern from uniform to intermittent mode can prevent material from overheating under the same power density. Supplying more microwave energy at the beginning of drying can increase the utilization of microwave energy while keeping temperature low within the particle. For a particle diameter of 4 mm, fluidization velocity of 2 m/s, inlet airflow temperature of 70°C and the bed area factor of 80, the drying time are 750 and 1000 s, respectively, for the two good operating conditions with on/off periods of 125/375 s and 375/375 s. The cumulative microwave energy absorbed by particles at the end of drying is 1415 and 2300 kJ/kg (dry basis), respectively.     

吸波材料辅助的液体物料微波冷冻干燥多物理场耦合模型

为了研究吸波材料辅助微波加热对传统冷冻干燥过程的强化作用,建立了多孔介质温度、浓度和电磁场耦合的多相传递模型;以烧结的碳化硅(SiC)为吸波材料、以甘露醇水溶液为待干料液进行了微波冷冻干燥实验,并测定了甘露醇固体的介电特性。模拟和实验结果均表明,吸波材料对初始非饱和多孔物料微波冷冻干燥具有显著的强化作用。初始非饱和样品微波冷冻干燥时间比传统冷冻干燥缩短了18%,比常规饱和样品传统冷冻干燥缩短了30%。模拟结果与实验数据吻合良好。这表明提出的新型干燥方法确实能够实现过程传热传质的同时强化。通过考察样品内部温度、饱和度和电场强度的实时分布,分析了微波冷冻干燥过程的传热传质和电磁波传播与耗散机理。在微波冷冻干燥过程中,初始非饱和样品累计吸收的辐射能和微波能的总和与传统冷冻干燥相当。这说明,该干燥方法只是提高了能量效率,从而大幅缩短了冷冻干燥时间。     

Effect of Pulsed Electric Field and Osmotic Dehydration Pretreatment on the Convective Drying of Carrot Tissue

The influence of pulsed electric field (PEF) and subsequent centrifugal osmotic dehydration (OD) on the convective drying behavior of carrot is investigated. The PEF was carried out at an intensity of E = 0.60 kV/cm and a treatment duration of t_PEF = 50 ms. The following centrifugal OD was performed in a sucrose solution of 65% (w/w) at 40°C for 0, 1, 2, or 4 h under 2400 × g. The drying was performed after the centrifugal OD for temperatures 40-60°C and at constant air rate (6 m³/h).

With the increase of OD duration the air drying time is reduced spectacularly. The dimensionless moisture ratio Xr = 0.1 is reached for PEF-untreated carrots after 370 min of air drying at 60°C in absence of centrifugal OD against 90 min of air drying after the 240 min of centrifugal OD. The PEF treatment reduces additionally the air drying time. The total time of dehydration operations can be shortened when OD time is optimized. For instance, the minimal time required to dehydrate untreated carrots until Xr = 0.1 is 260 min (120 min of OD at 40°C and 140 min of drying at 60°C). It is reduced to 230 min with PEF-treated carrots.

The moisture effective diffusivity D_eff is calculated for the convective air drying based on Fick's law. The centrifugal OD pretreatment increases drastically the value of D_eff. For instance, 4 h of centrifugal OD permitted increasing the value of D_eff from 0.93 · 10^-9 to 3.85 · 10^-9 m²/s for untreated carrots and from 1.17 · 10^-9 to 5.10 · 10^-9 m²/s for PEF-treated carrots.     

Analysis of Heat and Mass Transfer during High-Temperature Drying of Pinus radiata

This article describes the analysis of heat and mass transfer coefficients for a single board of Pinus radiata (D. Don) timber over a range of high temperature and superheated steam drying conditions. The calculated heat transfer coefficients were in the range 20 to 60 W m^-2 K^-1. The mass transfer coefficients were of the order of 2 × 10^-8 to 3 × 10^-7 kg m^-2 s^-1, based on the vapor pressure difference, and of the order of 0.002 to 0.04 m s^-1 (expressed in terms of mass transfer velocity) based on vapor concentration difference between the surface of the board and the bulk drying medium.     

Evaluation of Mass Transfer Resistances from Drying Experiments

A new approach to experimental evaluation of mass transfer resistances from drying experiments is proposed. A composite model of ginseng root mass transfer, based on one-dimensional treatment of diffusive and convective resistances as additive components of radial mass transfer, was developed. Mass transfer resistance was evaluated from a linear relationship between measured flux and thermodynamic driving force. Partitioning of mass transfer resistance into diffusive (core and skin) and convective (air boundary layer) resistances was done by modification of boundary conditions: (a) high (3 m/s) and low (1 m/s) air velocity; (b) skin removal. Total radial mass transfer resistance was evaluated as (146 ± 6) ∗ 10⁶ s/m at 38°C, significantly decreasing to (48 ± 1.5) ∗ 10⁶ s/m at 50°C. Boundary resistance was evaluated as (54 ± 5) ∗ 10⁶ s/m at 38°C and (26 ± 3) ∗ 10⁶ s/m at 50°C in the entire range of moisture contents. Core and skin resistances were both moisture dependent: core resistance increased from initial value of (6 ± 1) ∗ 10⁶ s/m to (61 ± 6) ∗ 10⁶ s/m toward the end of drying, whereas skin resistance decreased from initial value of (92 ± 5) ∗ 10⁶ s/m to (25 ± 5) ∗ 10⁶ s/m at the endpoint of drying. However, the sum of core and skin resistances, which represents composite diffusive resistance of intact ginseng root, was constant and independent of moisture content: (91 ± 4.6) ∗ 10⁶ s/m at 38°C and (22 ± 1.6) ∗ 10⁶ s/m at 50°C. The relationship between mass transfer resistance R and drying rate factor k = 1/RC was used for verification of the composite model.     

具有初始孔隙的多孔物料冷冻干燥

实验研究了具有一定孔隙的非饱和多孔物料对液体物料冷冻干燥过程的影响。以甘露醇为主要溶质的待干料液采用“液氮制冰激凌法”制备非饱和物料进行冷冻干燥,并与常规饱和的冷冻物料相比较。结果表明,非饱和冷冻物料确实能够显著地强化液体物料的冷冻干燥过程。干燥产品SEM形貌分析显示,初始非饱和冷冻物料具有连续均匀的固体骨架和孔隙,固体基质更加纤细,孔隙空间更大,可以大大减小传质阻力。考察物料内部各点的温度变化发现,初始非饱和物料内部冰晶确实发生整体升华,但仍然存在主要升华区域;非饱和多孔物料的冷冻干燥过程主要是传热控制,而常规饱和物料冷冻干燥主要是传质控制。操作压力对过程的影响可以忽略。采用辐射/导热组合加热方式可改善初始非饱和多孔物料冷冻干燥过程的传热,进一步缩短干燥时间。     

构建微波冷冻干燥质扩散系数的一种新方法

针对现有微波冷冻干燥模型中必须依靠实验以确定扩散系数的问题．提出一种构建扩散系的新方法。根据毛细管低压气体输运理论，利用物料本身的细微结构、气体分子平均自由程、气体状态参数和气体物性参数来构建扩散系数，在此基础上建立微波冷冻干燥模型。并结合牛肉的微波冷冻干燥行模型可靠性分析。结果表明，新建模型能够很好地描述微波冷冻干燥过程温度场的变化及其特征．升过程干燥曲线的理论值与实验值之间的相对误差小于10％。     

Heat and Mass Transfer During Fry-Drying of Sewage Sludge

Deep-frying, which consists of immersing a wet material in a large volume of hot oil, presents a process easily adaptable to dry rather than cook materials. A suitable material for drying is sewage sludge, which may be dried using recycled cooking oils (RCO) as frying oil. One advantage is that this prepares both materials for convenient disposal by incineration.

This study examines fry-drying of municipal sewage sludge using recycled cooking oil. The transport processes occurring during fry-drying were monitored through sample weight, temperature, and image analysis. Due to the thicker and wetter samples than the common fried foods, high residual moisture is observed in the sludge when the boiling front has reached the geometric center of the sample, suggesting that the operation is heat transfer controlled only during the first half of the process followed by the addition of other mechanisms that allow complete drying of the sample. A series of mechanisms comprising four stages (i.e., initial heating accompanied by a surface boiling onset, film vapor regime, transitional nucleate boiling, and bound water removal) is proposed. In order to study the effect of the operating conditions on the fry-drying kinetics, different oil temperatures (from 120 to 180°C), diameter (D = 15 to 25 mm), and initial moisture content of the sample (4.8 and 5.6 kg water·kg^-1 total dry solids) were investigated.     

具有预制孔隙多孔介质冷冻干燥的多相传递模型

基于局部质量非平衡假设,建立了多相多孔介质热、质耦合传递数学模型,理论验证具有预制孔隙的初始非饱和多孔物料对冷冻干燥过程的强化作用。模型考虑了多孔介质的吸湿效应,构建了3种吸附-解吸平衡关系。模型使用基于有限元法的COMSOL Multiphysics软件平台数值求解,并与实验数据进行了比较。结果表明,初始非饱和冷冻物料能够有效地强化冷冻干燥过程。采用不同函数形式的吸附-解吸平衡关系模拟的干燥曲线均与实验数据非常吻合。通过分析物料内部的饱和度、温度和质量源分布,探讨了初始非饱和物料冷冻干燥过程的传热传质机理。初始非饱和物料的干燥速率控制因素主要是传热。模拟考察环境辐射温度对冷冻干燥过程影响的结果表明,所建模型具有良好的预测能力。     

Optimization of the Freeze-Drying Cycle: A New Model for Pressure Rise Analysis

The principal aim of this study was to evaluate the Pressure Rise Analysis (PRA) method as a nonintrusive method for monitoring the product temperature during primary drying of the freeze-drying process of model pharmaceutical formulations. The principle of this method, based on the MTM method initially published by Milton et al.1 consisted in interrupting rapidly the water vapor flow from the sublimation chamber to the condenser chamber and by analyzing the resulting dynamics of the chamber total pressure increase. A new physical model, named PRA model, based on elementary heat and mass balance equations and on constitutive equations expressing the elementary fluxes, was proposed and validated in this study for interpreting the experimental pressure rise data. It was possible to identify very precisely the values of some key parameters of the freeze-drying process such as the ice sublimation interface temperature, the mass transfer resistance of the dried layer and the overall heat transfer coefficient of the vial. The identified ice front temperatures were compared with experimental data obtained from vial bottom temperatures measured by thin thermocouples during freeze-drying runs of 5% w/v mannitol solutions. These two sets of data were found consistent with a maximum difference of no more than 2°C. The dried layer mass transfer resistance increased linearly as a function of its thickness, and the values were coherent with the few literature data published for this system. The method also led to reliable values of the vial overall heat transfer coefficient of approximately 20 Wm^-2 K^-1 in accordance with the published data for this type of vials and these experimental freeze-drying conditions.     

Numerical investigation on freeze-drying of aqueous material frozen with pre-built pores

Freeze-drying of the initially porous frozen material with pre-built pores from liquid material was found experimentally to save drying time by over 30% with an initial saturation being 0.28 compared with the conventional operation with the initial saturation being 1, using mannitol as the solid material. In order to understand the mass and heat transfer phenomena of this novel process, a two-dimensional mathematical model of coupled mass and heat transfer was derived with reference to the cylindrical coordinate system. Three adsorption–desorption equilibrium relationships between the vapour pressure and saturation value namely, power-law, Redhead's style and Kelvin's style equation, were tested. Kelvin's style in exponential form of adsorption equilibrium relation gave an excellent agreement between the model prediction and experimental measurement when the equation parameter, γ, of 5000 was applied. Analyses of temperature and ice saturation profiles show that additional heat needs to be supplied to increase the sample temperature in order to promote the desorption process. Simulation also shows that there is a threshold initial porosity after which the drying time decreased with the increase in the initial porosity. Enhanced freeze-drying is expected to be achieved by simultaneously enhancing mass and heat transfer of the process.     

非饱和含湿多孔介质微波冷冻干燥过程传热传质分析

基于升华冷凝模型,对非饱和含湿多孔介质微波冷冻干燥过程作了数值计算．结果表明,干燥过程中不饱和含冰区内的冰饱和度有较大变化．通过与不考虑升华冷凝区相比较,表明升华冷凝区的存在不可忽略．     

From Laboratory Experiments to Design of a Conveyor-Belt Dryer via Mathematical Modeling

A conveyor-belt dryer for picrite has been modeled mathematically in this work. The necessary parameters for the system of equations were obtained from regression analysis of thin-layer drying data. The convective drying experiments were carried out at temperatures of 40, 60, 80, and 100°C and air velocities of 0.5 and 1.5 m/sec. To analyze the drying behavior, the drying curves were fitted to different semi-theoretical drying kinetics models such as those of Lewis, Page, Henderson and Pabis, Wang and Singh, and the decay models. The decay function (for second order reactions) gives better results and describes the thin layer drying curves quite well. The effective diffusivity was also determined from the integrated Fick's second law equation and correlated with temperature using an Arrhenius-type model. External heat and mass transfer coefficients were refitted to the empirical correlation using dimensionless numbers (J_h, J_D = m · Reⁿ) and their new coefficients were optimized as a function of temperature. The internal mass transfer coefficient was also correlated as a function of moisture content, air temperature, and velocity.     

初始非饱和多孔物料对冷冻干燥过程的影响

提出了“初始非饱和多孔物料冷冻干燥”的思想,从实验上验证具有一定初始孔隙的非饱和多孔物料对液体物料冷冻干燥过程的强化作用。设计、加工和组装了一套实验室规模的多功能冷冻干燥装置。采用“液氮制作冰激凌法”,将以甘露醇为主要溶质的液体物料制备成具有不同初始孔隙的冷冻物料。对于相同质量和相同湿含量的非饱和冷冻物料,在相同的操作条件下,进行冷冻干燥实验,并与常规冷冻干燥相比较。结果表明,初始非饱和物料对冷冻干燥过程确实具有显著的强化作用。非饱和冷冻物料(初始饱和度0.28)的干燥时间比常规冷冻物料(初始饱和度1.00)能够节省36.4%。初始饱和度越小,干燥时间越短,干燥产品的含水率越低。