Multiphysics conjugated model for freeze-drying of liquid solution assisted by wave-absorbing material

doi:10.11949/0438-1157.20190281

Abstract

Abstract:

To investigate the enhanced effect of wave-absorbing material assisted microwave heating on traditional freeze-drying, a multiphase transport mathematical model conjugating temperature field, concentration field and electromagnetic field was developed and numerically solved. The sintered silicon carbide (SiC) was used as the absorbing material and the mannitol aqueous solution was used. Microwave freeze-drying experiments of mannitol aqueous solution were carried out, and dielectric properties of mannitol solid powder were measured. Both numerical and experimental results show that using wave-absorbing material as the supporting pad of sample can effectively enhance the microwave freeze-drying process. Under the typical operating conditions, microwave freeze-drying time of the initially unsaturated material can be 18% and 30%, respectively, shorter than the traditional freeze-drying process of the initially unsaturated and conventionally saturated samples. Excellent agreements were received between experimental measurements and model predictions. This indicates that the proposed freeze-drying method can achieve the simultaneous enhancement of heat and mass transfer. Based on the profiles of temperature, ice saturation and electrical field strength, mechanisms of heat and mass transfer, as well as electromagnetic wave propagation and dissipation inside a sample were analyzed during drying. The accumulatively absorbed energy of radiation and microwave during drying was almost the same as those of traditional freeze-drying of the initially saturated and unsaturated samples. This demonstrates that the proposed method only increases the energy utilization so as to largely reduce the freeze-drying time.

Key words: microwave, wave-absorbing material, loss factor, saturation, drying, heat transfer, mass transfer

摘要：

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。

关键词: 微波, 吸波材料, 损耗因子, 饱和度, 干燥, 传热, 传质

CLC Number:

TQ 028.5

Jing YANG, Wei WANG, Shuo ZHANG, Chunfang SONG, Yujia TANG. Multiphysics conjugated model for freeze-drying of liquid solution assisted by wave-absorbing material[J]. CIESC Journal, 2019, 70(9): 3307-3319.

杨菁, 王维, 张朔, 宋春芳, 唐宇佳. 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[J]. 化工学报, 2019, 70(9): 3307-3319.

Figures/Tables 14

Fig.1 Physical model of microwave drying chamber

Fig.2 Schematic diagram of sample mold

Fig.3 Flow diagram of multifunctional microwave freeze drying system

Fig.4 Dielectric constant and loss factor of mannitol

Table 1 Input parameters used in simulation

Parameter	Value	Ref
c _b /(J/(kg·K))	1200	default^①
c _i /(J/(kg·K))	1930	[42]
c _s /(J/(kg·K))	1310	[43]
c _v /(J/(kg·K))	1886	[42]
e _b	0.5	default^①
e _i	0.97	[24]
e _s	0.6	[35]
ΔH /(J/kg)	2.839×10⁶	[43]
K _r/s^-1	300(S ₀=1.0)/30(S ₀=0.28)	[25]
?	0.8798(S ₀=1.0)/0.9631(S ₀=0.28)	Exp.
ε _r,b '	-12.36+0.087T	[33]
ε _r,i '	3.2	[44]
ε _r,s '	2.42894+0.00385T(℃)	Exp.
ε _r,v '	1	[45]
ε _r,b″	27.99	[46]
ε _r,i″	0.003	[44]
ε _r,s″	0.22+0.00038T(℃)	Exp.
ε _r,v″	0	[45]
λ _b /(W/(m·K))	450(300/T)^0.75	default^①
λ _i /(W/(m·K))	2.22	[42]
λ _s /(W/(m·K))	2.64	[47]
λ _v /(W/(m·K))	0.022	[42]
μ _r	1	—
μ _v/(kg/(m·s))	0.011(T/273)^1.5/(T+961)	[48]
ρ _b /(kg/m³)	3200	default^①
ρ _i/(kg/m³)	913	[42]
ρ _s /(kg/m³)	1489	[49]

Fig.5 Comparisons between experimental and predicted drying curves of different processes

Fig.6 Temperature distributions in initially unsaturated sample mold

Fig. 7 Saturation distributions in initially unsaturated sample

Fig.8 Electric field strength distribution on surfaces of waveguide, microwave cavity and sample mold at 0 s

Fig.9 Electric field strength distribution inside waveguide, microwave cavity and sample mold at 0 s

Fig. 10 Electric field strength distributions in initially unsaturated sample

Fig. 11 Electric field strength distribution in supporting pad (t=500 s)

Fig.12 Energies absorbed by two sample molds at 0 W and 1 W

Fig.13 Drying curves of initially unsaturated samples at different microwave powers

References 56

1	Liapis A I , Bruttini R . Freeze drying[M]//Mujumdar A S. Handbook of Industrial Drying. New York: Marcel Dekker, 2015: 259-282.
2	Nail S L , Jiang S , Chongprasert S , et al . Fundamentals of freeze-drying[M] //Nail S L , Akers M J . Development and Manufacture of Protein Pharmaceuticals. New York: Kluwer Academic & Plenum Publishers, 2002: 281-361.
3	Wang W , Chen G . Freeze drying with dielectric-material-assisted microwave heating[J]. AIChE Journal, 2007, 53(12): 3077-3088.
4	Wang W , Chen M , Chen G . Issues in freeze drying of aqueous solutions[J]. Chin. J. Chem. Eng., 2012, 20(3): 551-559.
5	Capozzi L C , Pisano R . Looking inside the ‘black box’: freezing engineering to ensure the quality of freeze-dried biopharmaceuticals[J]. Eur. J. Pharm. Biopharm., 2018, 129(8): 58-65.
6	Goshima H , Do G , Nakagawa K . Impact of ice morphology on design space of pharmaceutical freeze-drying[J]. J . Pharm. Sci., 2016, 105(6): 1920-1933.
7	Sitar A , Skrlec K , Voglar J , et al . Effects of controlled nucleation on freeze-drying lactose and mannitol aqueous solutions[J]. Drying Technol., 2018, 36(10): 1263-1272.
8	Bexiga N M , Bloise A C , Alencar A M , et al . Freeze-drying of ovalbumin-loaded carboxymethyl chitosan nanocapsules: impact of freezing and annealing procedures on physicochemical properties of the formulation during dried storage[J]. Drying Technol., 2018, 36(4): 400-417.
9	Pikal M J . Freeze drying[M]//Swarbrick J. Encyclopedia of Pharmaceutical Technology. 3nd ed. New York: Informa Healthcare, 2007: 1807-1833.
10	Wolff E , Gibert H , Rodolphe F . Vacuum freeze-drying kinetics and modelling of a liquid in a vial[J]. Chem. Eng. Process., 1989, 25(3): 153-158.
11	Hottot A , Vessot S , Andrieu J . A direct characterization method of the ice morphology. relationship between mean crystals size and primary drying times of freeze-drying processes[J]. Drying Technol., 2004, 22(8): 2009-2021.
12	Wang W , Chen G . Heat and mass transfer model of dielectric-material-assisted microwave freeze-drying of skim milk with hygroscopic effect[J]. Chem. Eng. Sci., 2005, 60(23): 6542-6550.
13	于凯, 王维, 潘艳秋, 等 . 初始非饱和多孔物料对冷冻干燥过程的影响[J]. 化工学报, 2013, 64 (9): 3110-3116.
	Yu K , Wang W , Pan Y Q , et al . Effect of initially unsaturated porous frozen material on freeze-drying[J]. CIESC Journal, 2013, 64 (9): 3110-3116.
14	Wang W , Hu D B , Pan Y Q , et al . Freeze-drying of aqueous solution frozen with prebuilt pores[J]. AIChE Journal, 2015, 61(6): 2048-2057.
15	Ambros S , Mayer R , Schumann B , et al . Microwave-freeze drying of lactic acid bacteria: Influence of process parameters on drying behavior and viability[J]. Innov. Food Sci. Emerg. Technol., 2018, 48(4): 90-98.
16	Ma Y H , Peltre P R . Freeze dehydration by microwave energy[J]. AIChE Journal, 1975, 21(2): 335-344.
17	Duan X , Zhang M , Mujumdar A S , et al . Microwave freeze drying of sea cucumber (Stichopus japonicus)[J]. J. Food Eng., 2010, 96(4): 491-497.
18	Wang R , Zhang M , Mujumdar A S . Effect of food ingredient on microwave freeze drying of instant vegetable soup[J]. LWT - Food Sci. Technol., 2010, 43(7): 1144-1150.
19	Wang W , Chen G . Numerical investigation on dielectric material assisted microwave freeze-drying of aqueous mannitol solution[J]. Drying Technol., 2003, 21(6): 995-1017.
20	Wang W , Chen G . Freeze drying with dielectric-material-assisted microwave heating[J]. AIChE Journal, 2007, 53(12): 3077-3088.
21	赵言冰 . 微波冷冻干燥过程传热传质的数值模拟[D]. 南京：东南大学, 2004.
	Zhao Y B . Numerical simulation of heat and mass transfer in microwave freeze-drying process[D]. Nanjing: Southeast University, 2004.
22	段续, 闫莎莎, 曾凡莲, 等 . 基于介电特性的白蘑菇微波冻干传热传质模拟[J]. 现代食品科技, 2016, 32(6): 177-182.
	Duan X , Yan S S , Zeng F L , et al . Simulation of heat and mass transfer during microwave freeze drying of white mushrooms based on dielectric property[J]. Modern Food Sci. Technol., 2016, 32(6): 177-182.
23	Halder A , Dhall A , Datta A K . An improved, easily implementable, porous media based model for deep-fat frying(Part I): Model development and input parameters[J]. Food Bioprod. Process., 2007, 85(3): 209-219.
24	Warning A D , Arquiza J M R , Datta A K . A multiphase porous medium transport model with distributed sublimation front to simulate vacuum freeze drying[J]. Food Bioprod. Process., 2015, 94(2): 637-648.
25	Halder A , Dhall A , Datta A K . Modeling transport in porous media with phase change: applications to food processing[J]. J.Heat Transf.-Trans.ASME, 2011, 133(3): 031010.
26	Meda V , Orsat V , Raghavan V . Microwave heating and the dielectric properties of foods[M] //Schubert H , Regier M . The Microwave Processing of Foods. Cambridge: Woodhead, 2005: 63-75.
27	Pu G Y , Song G L , Song C F , et al . Analysis of thermal effect using coupled hot-air and microwave heating at different position of potato[J]. Innov. Food Sci. Emerg. Technol., 2017, 41(3): 244-250.
28	Chen F , Warning A D , Datta A K , et al . Susceptors in microwave cavity heating: modeling and experimentation with a frozen pie[J]. J. Food Eng., 2017, 195(4): 191-205.
29	Bird R B , Stewart W E , Lightfoot E N . Transport Phenomena[M]. New York: John Willey & Sons, 2002: 488-508.
30	张朔, 王维, 李强强, 等 . 具有预制孔隙的维生素C水溶液微波冷冻干燥[J]. 化工学报, 2019, 70(6): 2129-2138.
	Zhang S , Wang W , Li Q Q , et al . Microwave freeze-drying of vitamin C solution frozen with preformed pores[J]. CIESC Journal, 2019, 70(6): 2129-2138.
31	Dong S , Zhang X H , Zhang D Y , et al . Strong effect of atmosphere on the microstructure and microwave absorption properties of porous SiC ceramics [J]. J.Eur.Ceram. Soc., 2018, 38(1): 29-39.
32	赵延强, 王维, 潘艳秋, 等 . 具有初始孔隙的多孔物料冷冻干燥[J]. 化工学报, 2015, 66(2): 504-511.
	Zhao Y Q , Wang W , Pan Y Q , et al . Freeze-drying of porous frozen material with initial porosity[J]. CIESC Journal, 2015, 66(2): 504-511.
33	Polaert I , Benamara N , Tao J , et al . Dielectric properties measurement methods for solids of high permittivities under microwave frequencies and between 20 and 250℃[J]. Chem. Eng. Process., 2017, 122(12): 339-345.
34	Song C F , Sang T , Li Z F , et al . Dielectric properties of blackberries as related to microwave drying control[J]. Int.J.Food Eng., 2017, 13(12): 1-8.
35	牛利娇, 王维, 潘思麒, 等 . 具有预制孔隙多孔介质冷冻干燥的多相传递模型[J]. 化工学报, 2017, 68(5): 1833-1844.
	Niu L J , Wang W , Pan S Q , et al . Multiphase transport model for freeze-drying of porous media with prefabricated porosity [J]. CIESC Journal, 2017, 68(5): 1833-1844.
36	Nakagawa K , Hottot A , Vessot S , et al . Modeling of freezing steps during freeze-drying of drugs in vials[J]. AIChE Journal, 2007, 53(5): 1362-1372.
37	Chen M , Wang W , Pan Y Q , et al . 1D and 2D numerical verification on freeze drying of initially porous material frozen from aqueous solution[C]//Chen X D, Mujumdar A S. Proc.18th Intern. Drying Symp. Xiamen, China: XMU, 2012
38	Geankoplis C J . Transport Processes and Unit Operations[M]. 3nd ed.NJ: Englewood Cliffs, 1993: 462-466.
39	Warning A , Dhall A , Mitrea D , et al . Porous media based model for deep-fat vacuum frying potato chips[J]. J. Food Eng., 2012, 110(3): 428-440.
40	Edmonton B . Brook Taylor[M] // Gowers T , Barrow-Green J , Leader I . The Princeton Companion to Mathematics. Princeton: Princeton University Press, 2008: 745-746.
41	Murphy D M , Koop T . Review of the vapour pressures of ice and super cooled water for atmospheric applications [J]. Q. J. R. Meteorol. Soc., 2005, 131(608): 1539-1565.
42	Eckert E R G , Drake R M . Thermophysical Properties, Analysis of Heat and Mass Transfer[M]. New York: McGraw-Hill, 1987: 767-783.
43	Liley P E . Physical and chemical data[M] // Perry H R , Green D W , Maloney J O . Perry’s Chemical Engineers’ Handbook. New York: McGraw-Hill, 1997: 40-304.
44	Tang J . Dielectric properties of foods[M] //Schubert H , Regier M . The Microwave Processing of Foods. Cambridge: Woodhead, 2005: 22-40.
45	Zhu H C , Gulati T , Datta A K , et al . Microwave drying of spheres: coupled electromagnetics-multiphase transport modeling with experimentation(Part Ⅰ): Model development and experimental methodology[J]. Food Bioprod. Process., 2015, 96(4): 314-325.
46	Basak T , Aparna K , Meenakshi A , et al . Effect of ceramic supports on microwave processing of porous food samples[J]. Int. J. Heat Mass Transf., 2006, 49(23/24): 4325-4339.
47	Wang W , Hu D P , Pan Y Q , et al . Numerical investigation on freeze-drying of aqueous material frozen with pre-built pores[J]. Chin.J. Chem.Eng., 2016, 24(1): 116-125.
48	Idelchik I E . General information and element of aerodynamics and hydraulic of pressure systems[M] //Steinberg M O , Malyavskaya G R , Martynenko O G . Handbook of Hydraulic Resistance. Florida: CRC Press, 1994: 9-12.
49	Lide D R . Handbook of Data on Organic Compounds[M]. Florida: CRC Press, 1994: 3338.
50	李恒乐, 王维, 李强强, 等 . 具有预制孔隙多孔物料的冷冻干燥[J]. 化工学报, 2016, 67(7): 2857-2863.
	Li H L , Wang W , Li Q Q , et al . Freeze-drying of porous frozen material with prefabricated porosity [J]. CIESC Journal, 2016, 67(7): 2857-2863.
51	崔政伟, 陈丽君, 宋春芳, 等 . 热风微波耦合干燥技术和设备的研究进展[J]. 食品与生物技术学报, 2014, 33(11): 1121-1128.
	Cui Z W , Chen L J , Song C F , et al . Advances in coupled hot-air and microwave drying technique and equipment[J]. J . Food Sci. Biotech., 2014, 33(11): 1121-1128.
52	Hossan M R , Byun D , Dutta P . Analysis of microwave heating for cylindrical shaped objects[J]. Int.J. Heat Mass Transf., 2010, 53(23/24): 5129-5138.
53	Knoerzer K , Regier M , Schubert H . A computational model for calculating temperature distributions in microwave food applications[J]. Innov. Food Sci. Emerg. Technol., 2008, 9(3): 374-384.
54	陈又鲜 . 微波炉电磁场仿真设计匹配研究[D]. 成都: 电子科技大学, 2013.
	Chen Y X . Research about simulation design match of elecromagnetic field in microwave oven[D]. Chengdu: University of Electronic Science and Technology of China, 2013.
55	谢晓影, 乔秀臣 . 微波烧结的“热点”形成机制[J]. 微波学报, 2016, 32(5): 84-88.
	Xie X Y , Qiao X C . Mechanism of “hot spot” generation in microwave sintering process[J]. Journal of Microwaves, 2016, 32(5): 84-88.
56	Regier M , Schubert H . Introducing microwave processing of food: principles and technologies[M] //Schubert H , Regier M . The Microwave Processing of Foods. Cambridge: Woodhead, 2005: 3-20.

[1]	Shuangxing ZHANG, Fangchen LIU, Yifei ZHANG, Wenjing DU. Experimental study on phase change heat storage and release performance of R-134a pulsating heat pipe [J]. CIESC Journal, 2023, 74(S1): 165-171.
[2]	Yifei ZHANG, Fangchen LIU, Shuangxing ZHANG, Wenjing DU. Performance analysis of printed circuit heat exchanger for supercritical carbon dioxide [J]. CIESC Journal, 2023, 74(S1): 183-190.
[3]	Aiqiang CHEN, Yanqi DAI, Yue LIU, Bin LIU, Hanming WU. Influence of substrate temperature on HFE7100 droplet evaporation process [J]. CIESC Journal, 2023, 74(S1): 191-197.
[4]	Mingxi LIU, Yanpeng WU. Simulation analysis of effect of diameter and length of light pipes on heat transfer [J]. CIESC Journal, 2023, 74(S1): 206-212.
[5]	Zhiguo WANG, Meng XUE, Yushuang DONG, Tianzhen ZHANG, Xiaokai QIN, Qiang HAN. Numerical simulation and analysis of geothermal rock mass heat flow coupling based on fracture roughness characterization method [J]. CIESC Journal, 2023, 74(S1): 223-234.
[6]	Jingwei CHAO, Jiaxing XU, Tingxian LI. Investigation on the heating performance of the tube-free-evaporation based sorption thermal battery [J]. CIESC Journal, 2023, 74(S1): 302-310.
[7]	Di WU, Bin HU, Ruzhu WANG, Junyu LIANG. Performance analysis of water vapor quasi-saturated compression high temperature heat pump system [J]. CIESC Journal, 2023, 74(S1): 45-52.
[8]	Cheng CHENG, Zhongdi DUAN, Haoran SUN, Haitao HU, Hongxiang XUE. Lattice Boltzmann simulation of surface microstructure effect on crystallization fouling [J]. CIESC Journal, 2023, 74(S1): 74-86.
[9]	Lei WU, Jiao LIU, Changcong LI, Jun ZHOU, Gan YE, Tiantian LIU, Ruiyu ZHU, Qiuli ZHANG, Yonghui SONG. Catalytic microwave pyrolysis of low-rank pulverized coal for preparation of high value-added modified bluecoke powders containing carbon nanotubes [J]. CIESC Journal, 2023, 74(9): 3956-3967.
[10]	Yitong LI, Hang GUO, Hao CHEN, Fang YE. Study on operating conditions of proton exchange membrane fuel cells with non-uniform catalyst distributions [J]. CIESC Journal, 2023, 74(9): 3831-3840.
[11]	Yubing WANG, Jie LI, Hongbo ZHAN, Guangya ZHU, Dalin ZHANG. Experimental study on flow boiling heat transfer of R134a in mini channel with diamond pin fin array [J]. CIESC Journal, 2023, 74(9): 3797-3806.
[12]	Cong QI, Zi DING, Jie YU, Maoqing TANG, Lin LIANG. Study on solar thermoelectric power generation characteristics based on selective absorption nanofilm [J]. CIESC Journal, 2023, 74(9): 3921-3930.
[13]	Ke LI, Jian WEN, Biping XIN. Study on influence mechanism of vacuum multi-layer insulation coupled with vapor-cooled shield on self-pressurization process of liquid hydrogen storage tank [J]. CIESC Journal, 2023, 74(9): 3786-3796.
[14]	Tianhua CHEN, Zhaoxuan LIU, Qun HAN, Chengbin ZHANG, Wenming LI. Research progress and influencing factors of the heat transfer enhancement of spray cooling [J]. CIESC Journal, 2023, 74(8): 3149-3170.
[15]	Yue YANG, Dan ZHANG, Jugan ZHENG, Maoping TU, Qingzhong YANG. Experimental study on flash and mixing evaporation of aqueous NaCl solution [J]. CIESC Journal, 2023, 74(8): 3279-3291.