范德华力对磁场流化纳米颗粒运动影响

doi:10.11949/0438-1157.20240078

摘要/Abstract

摘要：

纳米颗粒存在较强的颗粒间作用力。在传统磁化模型基础上添加范德华力模型，采用有限体积法（FVM）与离散单元法（DEM）进行数值模拟，运用Fluent-EDEM双平台耦合进行气固两相流分析，研究不同磁场方向与不同磁感应强度下范德华力对纳米颗粒运动的影响。结果表明，纳米颗粒间的范德华力对磁场流化床中颗粒运动的影响不可忽略，其在低磁通量密度下与磁化力之间存在明显牵制关系；磁场角度为0°时纳米颗粒分层现象明显，随场强增大分层效果逐渐缓解；范德华力也会在一定程度上促使颗粒运动方向发生偏转。范德华力模型的引入进一步拓宽了磁化模型的适用范围，为研究纳米颗粒在磁场中的运动提供数据支持。

关键词: 纳米粒子, 范德华力, 流态化, 聚集, 磁场流化床, 修正磁化模型

Abstract:

The nanoparticles exhibit significant intergranular cohesive forces. The van der Waals forces between nanoparticles in a magnetic fluidized bed are considered and the modified magnetization model is further improved. The finite volume method (FVM) and discrete element method (DEM) were used for numerical simulation, and the gas-solid two-phase flow was analyzed by using the coupling of Fluent-EDEM dual platform. The results indicate that the impact of van der Waals forces between nanoparticles on particle movement in magnetic fluidized beds cannot be overlooked, and there exists a distinct inhibitory relationship between van der Waals forces and magnetization forces at low magnetic flux density. The stratification of nanoparticles becomes more pronounced at a magnetic field angle of 0°, and the stratification effect gradually diminishes with increasing field intensity. The van der Waals force also deflects the direction of particle motion to a certain extent. The introduction of van der Waals force model further broadens the application range of magnetization model and provides data support for studying the motion of nanoparticles in magnetic field.

Key words: nanoparticles, van der Waals force, fluidization, aggregation, magnetic fluidized bed, modified magnetization model

中图分类号:

O359

陈巨辉, 安然, 李丹, 高浩铭, 张坤. 范德华力对磁场流化纳米颗粒运动影响[J]. 化工学报, DOI: 10.11949/0438-1157.20240078.

Juhui CHEN, Ran AN, Dan LI, Haoming GAO, Kun ZHANG. Effect of van der Waals forces on the motion of magnetic field fluidized nanoparticles[J]. CIESC Journal, DOI: 10.11949/0438-1157.20240078.

图/表 15

图1 颗粒受力简略示意图

Fig.1 Sketch diagram of particle force

图2 模型网格图

Fig.2 The mesh of model

表1 网格无关性检验

Table 1 Grid independence test

最小网格尺寸	网格数量(个)	总动能(10^-10·J)
1R	6229	0.0642
2R	4163	0.0471
3R	2248	0.0243
4R	1920	0.0238
5R	863	0.0386
6R	664	0.0497

表2 模拟参数

Table 2 Analog parameter

名称	实验参数	模拟参数
颗粒直径/ m	1.7e-8	1.7e-8
颗粒密度/(kg/m³)	850	850
气相密度/(kg/m³)	1.29	1.29
注入颗粒数量	-	800
纳米颗粒磁导率/(H/m)	8.3	8.3
杨氏模量/ GPa	68.95	68.95
泊松比	0.33	0.33
颗粒-颗粒摩擦系数	0.3	0.3
颗粒弹性刚度/(N/m)	800	800
颗粒-壁面摩擦系数	0.3	0.3
墙壁弹性刚度/(N/m)	800	800
阻尼系数	0.05	0.05

表3 模拟工况

Table 3 Simulated working condition

B₀/(T) β/(deg)	0.01	0.0125	0.02
0	C1	C5	C9
30	C2	C6	C10
60	C3	C7	C11
90	C4	C8	C12

图3 压降变化

Fig.3 Pressure drop

图4 归一化信号熵变化

Fig.4 Change of normalized signal entropy

图5 B0=0.01T，颗粒分布

Fig.5 B0=0.01T, Particle distribution

图6 1s时刻颗粒分布

Fig.6 Particle distribution map at 1s

图7 0.01T时无范德华力颗粒总动能

Fig.7 Total kinetic energy of particles without van der Waals force at 0.01T

图8 加入范德华力后总动能变化曲线

Fig.8 Change curve of total kinetic energy after adding van der Waals force

图9 总动能变化曲线

Fig.9 Total kinetic energy change curve

图10 1s时刻颗粒速度矢量图

Fig.10 Particle velocity vector diagram at 1s

图11 1s时刻颗粒速度矢量图

Fig.11 Particle velocity vector diagram at 1s

图12 颗粒角速度变化曲线

Fig.12 Particle angular velocity change curve

参考文献 32

1	Fan G D, Song Y Q, Xia M Q, et al. Photocatalytic inactivation of algae in a fluidized bed photoreactor with an external magnetic field[J]. Journal of Environmental Management, 2022, 307:114552.
2	Hao W K, Zhu Q H. Operating range of magnetic stabilization flow regime for magnetized fluidized bed with Geldart-B magnetizable and nonmagnetizable particles[J]. Particuology, 2022, 60: 90-98.
3	林檬, 陈国, 赵珺. 磁辅助生物反应器研究进展[J]. 化工进展, 2014, 33(5): 1252-1258, 1320.
	Lin M, Chen G, Zhao J. Research progress of magnetically assisted bioreactor[J]. Chemical Industry and Engineering Progress, 2014, 33(5): 1252-1258, 1320.
4	Bahramian A, Olazar M. Evaluation of elastic and inelastic contact forces in the flow regimes of Titania nanoparticle agglomerates in a bench-scale conical fluidized bed: a comparative study of CFD-DEM simulation and experimental data[J]. Chemical Engineering Research and Design, 2021, 176: 34-48.
5	Hoorijani H, Zarghami R, Nosrati K, et al. Investigating the hydrodynamics of vibro-fluidized bed of hydrophilic titanium nanoparticles[J]. Chemical Engineering Research and Design, 2021, 174: 486-497.
6	Pan F, Du Z, Li S F, et al. Preparation of nano-sized tungsten carbide via fluidized bed[J]. Chinese Journal of Chemical Engineering, 2020, 28(3): 923-932.
7	Liu H P, Wang S W. Fluidization behaviors of nanoparticle agglomerates with high initial bed heights[J]. Powder Technology, 2021, 388: 122-128.
8	Chaouki J, Chavarie C, Klvana D, et al. Effect of interparticle forces on the hydrodynamic behaviour of fluidized aerogels[J]. Powder Technology, 1985, 43(2): 117-125.
9	Liu D Y, van Wachem B G M, Mudde R F, et al. Characterization of fluidized nanoparticle agglomerates by using adhesive CFD-DEM simulation[J]. Powder Technology, 2016, 304: 198-207.
10	Liu D Y, van Wachem B G M, Mudde R F, et al. An adhesive CFD-DEM model for simulating nanoparticle agglomerate fluidization[J]. AIChE Journal, 2016, 62(7): 2259-2270.
11	王垚, 金涌, 魏飞, 等. 原生纳米级颗粒的聚团散式流态化[J]. 化工学报, 2002, 53(4): 344-348.
	Wang Y, Jin Y, Wei F, et al. Agglomerate particulate fluidization of primary nano-particles[J]. Journal of Chemical Industry and Engineering (China), 2002, 53(4): 344-348.
12	Vimal T, Pandey S, Gupta S K, et al. Manifestation of strong magneto-electric dipolar coupling in ferromagnetic nanoparticles–FLC composite: evaluation of time-dependent memory effect[J]. Liquid Crystals, 2018, 45(5): 687-697.
13	Maniotis N, Nazlidis A, Myrovali E, et al. Estimating the effective anisotropy of ferromagnetic nanoparticles through magnetic and calorimetric simulations[J]. Journal of Applied Physics, 2019, 125(10): 103903.
14	Ganzha V L, Saxena S C. Hydrodynamic behavior of magnetically stabilized fluidized beds of magnetic particles[J]. Powder Technology, 2000, 107(1/2): 31-35.
15	Jovanovic G N, Sornchamni T, Atwater J E, et al. Magnetically assisted liquid–solid fluidization in normal and microgravity conditions: experiment and theory[J]. Powder Technology, 2004, 148(2/3): 80-91.
16	Espin M J, Quintanilla M A S, Valverde J M. Magnetic stabilization of fluidized beds: Effect of magnetic field orientation[J]. Chemical Engineering Journal, 2017, 313: 1335-1345.
17	Zhu Q H, Li H Z, Zhu Q S, et al. Hydrodynamic study on magnetized fluidized beds with Geldart-B magnetizable particles[J]. Powder Technology, 2014, 268: 48-58.
18	Ishii T, Yamakawa H, Kanaki T, et al. Large terahertz magnetization response in ferromagnetic nanoparticles[J]. Applied Physics Letters, 2019, 114(6): 062402.
19	Prischepa S, Danilyuk A. Anisotropic temperature-dependent interaction of ferromagnetic nanoparticles embedded inside CNT[J]. International Journal of Nanoscience, 2019, 18(3n04): 1940015.
20	Abu-Bakr A F, Zubarev A Y. Effect of ferromagnetic nanoparticles aggregation on magnetic hyperthermia[J]. The European Physical Journal Special Topics, 2020, 229(2): 323-329.
21	Ku J G, Xia J, Li J Z, et al. Accurate calculation of major forces acting on magnetic particles in a high-gradient magnetic field: a 3D finite element analysis[J]. Powder Technology, 2021, 394: 767-774.
22	Vogel F, Pelteret J P, Kaessmair S, et al. Magnetic force and torque on particles subject to a magnetic field[J]. European Journal of Mechanics-A/Solids, 2014, 48: 23-37.
23	Pinto-Espinoza J. Dynamic behavior of ferromagnetic particles in a liquid-solid magnetically assisted fluidized bed (MAFB): theory, experiment, and CFD-DPM simulation[D]. Corvallis: Oregon State University, 2002.
24	Hao Z H, Li X, Lu H L, et al. Numerical simulation of particle motion in a gradient magnetically assisted fluidized bed[J]. Powder Technology, 2010, 203(3): 555-564.
25	陈巨辉, 安然, 舒崚峰, 等. 修正磁化模型的多组分铁磁性颗粒运动研究[J]. 力学学报, 2024, 56(3): 740-750.
	Chen J H, An R, Shu L F, et al. Study on motion of multi-component ferromagnetic particles with modified magnetization model[J]. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(3): 740-750.
26	Rosensweig R E. Magnetic stabilization of the state of uniform fluidization[J]. Industrial & Engineering Chemistry Fundamentals, 1979, 18(3): 260-269.
27	Chen J H, An R, Li D, et al. A modified Pinto-Espinoza magnetization model for studying on motion characteristics of ferromagnetic particles[J]. Journal of Magnetism and Magnetic Materials, 2024, 589: 171539.
28	Greenwood J A. Adhesion of elastic spheres[J]. Proceedings of the Royal Society of London A, 1997, 453: 1277-1297.
29	Krupp H. Particle adhesion theory and experiment[J]. Advances in Colloid and Interface Science, 1967, 1(2): 111-239.
30	He Y, Muller F, Hassanpour A, et al. A CPU-GPU cross-platform coupled CFD-DEM approach for complex particle-fluid flows[J]. Chemical Engineering Science, 2020, 223:115712.
31	Zhu Q H, Li H Z, Zhu Q S, et al. Hydrodynamic behavior of magnetized fluidized beds with admixtures of Geldart-B magnetizable and nonmagnetizable particles[J]. Particuology, 2016, 29: 86-94.
32	Karimi F, Haghshenasfard M, Sotudeh-Gharebagh R, et al. Multiscale characterization of nanoparticles in a magnetically assisted fluidized bed[J]. Particuology, 2020, 51: 64-71.

[1]	申州洋, 薛康, 刘青, 史成香, 邹吉军, 张香文, 潘伦. 吸热型纳米流体燃料研究进展[J]. 化工学报, 2024, 75(4): 1167-1182.
[2]	赵文琪, 邓燕君, 朱春英, 付涛涛, 马友光. 纳米粒子稳定的Pickering乳液及其液滴聚并动力学研究进展[J]. 化工学报, 2024, 75(1): 33-46.
[3]	赵亚欣, 张雪芹, 王荣柱, 孙国, 姚善泾, 林东强. 流穿模式离子交换层析去除单抗聚集体[J]. 化工学报, 2023, 74(9): 3879-3887.
[4]	仪显亨, 周骛, 蔡小舒, 蔡天意. 光纤后向动态光散射测量纳米颗粒的浓度适用范围研究[J]. 化工学报, 2023, 74(8): 3320-3328.
[5]	王新悦, 王俊杰, 曹思贤, 王翠, 李灵坤, 吴宏宇, 韩静, 吴昊. 玻璃内包材界面修饰对机械应力诱导的单克隆抗体聚集体形成的影响[J]. 化工学报, 2023, 74(6): 2580-2588.
[6]	李勇, 高佳琦, 杜超, 赵亚丽, 李伯琼, 申倩倩, 贾虎生, 薛晋波. Ni@C@TiO₂核壳双重异质结的构筑及光热催化分解水产氢[J]. 化工学报, 2023, 74(6): 2458-2467.
[7]	侯文起, 孙彦, 董晓燕. 碱化修饰甲状腺素运载蛋白显著增强对淀粉样β蛋白聚集的抑制作用[J]. 化工学报, 2023, 74(5): 2100-2110.
[8]	陈毓明, 历伟, 严翔, 王靖岱, 阳永荣. 初生态聚乙烯聚集态结构调控研究进展[J]. 化工学报, 2023, 74(2): 487-499.
[9]	周惠敏, 田莹, 刘思亿, 邹佳航, 张润泽, 贺常晴, 何林, 隋红. 沥青质分子缔合作用机制、表征、理论计算与应用研究进展[J]. 化工学报, 2023, 74(10): 3995-4019.
[10]	于晓宇, 安瑛, 左夏华, 李凯, 张锋华, 焦志伟, 杨卫民. 旋流作用下水基炭黑纳米流体集热性能研究[J]. 化工学报, 2023, 74(10): 4097-4108.
[11]	黄心童, 耿宇昊, 刘恒源, 陈卓, 徐建鸿. 微流控制备新型功能纳米粒子研究进展[J]. 化工学报, 2023, 74(1): 355-364.
[12]	曲国娟, 江涛, 刘涛, 马骧. 超分子策略调控金纳米团簇的发光行为[J]. 化工学报, 2023, 74(1): 397-407.
[13]	张炜, 李昊阳, 徐纯刚, 李小森. 气体水合物生成微观机理及分析方法研究进展[J]. 化工学报, 2022, 73(9): 3815-3827.
[14]	王凯玥, 马永丽, 李琛, 刘明言. 气液固微型流化床的气液传质系数[J]. 化工学报, 2022, 73(8): 3529-3540.
[15]	张鑫, 许蕊, 路馨语, 牛永安. SiO₂@BiOCl-Bi₂₄O₃₁Cl₁₀核壳微球的合成及光催化[J]. 化工学报, 2022, 73(8): 3636-3646.