Modeling of Electrostatic Interaction and Safety Boundary Between Coated Energetic Explosive Particles Based on Re-expansion Method

doi:10.12382/bgxb.2023.1179

Abstract

Abstract:

The electrostatic safety boundary between coated energetic explosive particles in the production process is studied.A theoretical model of electrostatic interaction between charged coated energetic explosive particles is established by using the re-expansion method.The boundaries of charge density and electric field intensity threshold for electrostatic discharge of coated energetic explosive particle are defined based on the modified Paschen’s law. The influences of key particle structure and electrical properties on electrostatic agglomeration and discharge are discussed.The results show that the polarization effect of the coated medium enhances the electric field in the gap and attractive force,resulting in a like-charge attraction phenomenon of charged particles and exacerbating the discharge risk.Under the same charge,the attractive force between the coated active metal conductor particles is much higher than that between coated single-component explosive dielectric particles.When the surface charge density of coated active metal conductor particle is ±5.0μC/m²,the electric field exceeds the air breakdown threshold.For the coated dielectric particles,the electric field surpasses the breakdown threshold only when the surface charge density reaches ±50μC/m².Therefore,the coated active metal conductor particles possess less electrostatic safety than that of coated single-component dielectric particles,and the greater risk of electrostatic agglomeration and electrostatic discharge.

Key words: energetic explosive, electrostatic field, breakdown threshold, electrostatic discharge, electrostatic safety boundary

CLC Number:

TJ55

FENG Yue, ZHOU Zilong, WU Chengcheng, GUO Xueyong, ZHANG Bo, WANG Hao, WANG Shuo. Modeling of Electrostatic Interaction and Safety Boundary Between Coated Energetic Explosive Particles Based on Re-expansion Method[J]. Acta Armamentarii, 2025, 46(1): 231179-.

Figures/Tables 14

Fig.1 Schemaric diagram of two coated spherical explosive particle structures

Fig.2 Geometrical configuration of two-dimensional axisymmetric model

Fig.3 Potential distribution of coated explosive particle with a dielectric core

Fig.4 Potential distribution of coated explosive particle with a conductor core

Fig.5 Variation of electric field norm with charge density on the outer surface of Particle 2

Fig.6 Electric field norm distribution around coated explosive particles with same radius

Fig.7 Electric field norm distribution around coated explosive particles with different radii

Fig.8 Distribution of electric field norm along central axis (σc1=-σc2=1.0 μC/m2)

Fig.9 Electrostatic force between two coated dielectric-core particles versus dimensionless gap (σc1=1.0μC/m2)

Fig.10 Electrostatic force between two coated conducting-core particles versus dimensionless gap(σc1=1.0μC/m2)

Fig.11 Independence of electrostatic force on σc2 with the constant total amount of charge

Fig.12 Paschen’s curve andmodified Paschen’s curve

Fig.13 Variation of maximum electric field with gap for different surface charge densities

Table 1 Comparison of electrostatic interaction models

模型	优点	缺点
基于多极镜像法的模型^[18]	解形式简单	无法建模双颗粒系统
基于球坐标系中多极展开法的模型^[14]	物理意义明确可以建模包覆结构药粒	解收敛性较差静电力求解需要计算二重积分矩阵,形式非常复杂
基于双球坐标系中多极展开法的模型^[15]	物理意义明确可以求解球-平面系统	解收敛性较差无法建模包覆结构药粒电场求解需要计算二元变系数差分方程,形式非常复杂
本文提出的基于再展开法的模型	解形式简单解收敛性较好物理意义明确可以建模包覆结构药粒	无法求解球-平面系统

References 29

[1]	王晓峰. 关于不敏感弹药的几点认识[J]. 火炸药学报, 2022, 45(3):285-289. doi: 10.14077/j.issn.1007-7812.202112003
	WANG X F. Some opinions about insensitive munition[J]. Chinese Journal of Explosives & Propellants, 2022, 45(3):285-289. (in Chinese)
[2]	吴成成, 王正宏, 李世伟, 等. CL-20基压装炸药结构成型载体的设计及其应用[J]. 火炸药学报, 2022, 45(3):388-395. doi: 10.14077/j.issn.1007-7812.202204020
	WU C C, WANG Z H, LI S W, et al. Design andapplication of CL-20-based pressed explosives structure forming carrier[J]. Chinese Journal of Explosives & Propellants, 2022, 45(3):388-395. (in Chinese)
[3]	徐洋, 黎勤, 王团盟. Estane/Al复合钝感包覆CL-20的研究[J]. 火工品, 2021(6):46-49.
	XU Y, LI Q, WANG T M. Research oninsensitivity of CL-20 coated with Estane/Al[J]. Initiators & Pyrotechnics, 2021(6):46-49. (in Chinese)
[4]	闫涛, 任慧, 马爱娥, 等. 氟橡胶包覆层对纳米铝粉性能的影响研究[J]. 兵工学报, 2019, 40(8):1611-1617. doi: 10.3969/j.issn.1000-1093.2019.08.008
	YAN T, REN H, MA A E, et al. Effect of fluororubber coating on the properties of nano-aluminum powders[J]. Acta Armamentarii, 2019, 40(8):1611-1617. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.08.008
[5]	魏华. CL-20的表面钝感包覆研究[D]. 北京: 北京理工大学, 2020.
	WEI H. Research onreduced sensitivity of CL-20 with surface coating[D]. Beijing: Beijing Institute of Technology, 2017. (in Chinese)
[6]	SONG W K, ZHAI H, JI W, et al. Poly(aluminum chloride) shell-desensitized cyclotrimethylenetrinitramine explosive core[J]. Materials Chemistry and Physics, 2022,276:125335.
[7]	ZHANG H L, JIAO Q J, ZHAO W J, et al. Enhancedcrystal stabilities of ε-CL-20 via core-shell structured energetic composites[J]. Applied Sciences-Basel, 2020, 10(8):2663.
[8]	刘尚合, 武占成. 静电放电及危害防护[M]. 北京: 北京邮电大学出版社, 2004.
	LIU S H, WU Z C. Electrostatic discharge and hazard protection[M]. Beijing: Beijing University of Posts and Telecommunications Press, 2004. (in Chinese)
[9]	TANG T B, CHAUDHRI M M. Electron-induced decomposition and time-dependent breakdown of ionic solids:an experimental study on silver azide[J]. Physical Review B, 1984, 30(10):6154.
[10]	卫水爱, 白春华, 李春光. 发射药生产过程中静电锥体放电规律数值模拟研究[J]. 兵工学报, 2017, 38(5) 892-899. doi: 10.3969/j.issn.1000-1093.2017.05.008
	WEI S A, BAI C H, LI C G. Simulation of electrostatic cone discharge in propellant production process[J]. Acta Armamentarii, 2017, 38(5):892-899. (in Chinese)
[11]	BAILEY A G. Charging of solids and powders[J]. Journal of Electrostatics, 1993,30:167-180.
[12]	WISTROM A O, KHACHATOURIAN A V. Calibration of the electrostatic force between spheres at constant potential[J]. Measurement Science and Technology, 1999, 10(12):1296.
[13]	NAKAJIMA Y, SATO T. Calculation of electrostatic force between two charged dielectric spheres by the re-expansion method[J]. Journal of Electrostatics, 1999, 45(3):213-226.
[14]	BICHOUTSKAIA E, BOATWRIGHT A L, KHACHATOURIAN A, et al. Electrostatic analysis of the interactions between charged particles of dielectric materials[J]. The Journal of Chemical Physics, 2010, 133(2):024105.
[15]	KHACHATOURIAN A, CHAN H-K, STACE A J, et al. Electrostatic force between a charged sphere and a planar surface:a general solution for dielectric materials[J]. The Journal of Chemical Physics, 2014, 140(7):074107.
[16]	PéREZ A T, FERNáNDEZ-MATEO R. Electric force between a dielectric sphere and a dielectric plane[J]. Journal of Electrostatics, 2021,112:103601.
[17]	COX B J, THAMWATTANA N, HILL J M. Electrostatic force between coated conducting spheres with applications to electrorheological nanofluids[J]. Journal of Electrostatics, 2007, 65(10/11):680-688.
[18]	LINDGREN E B, CHAN H K, STACE A J, et al. Progress in the theory of electrostatic interactions between charged particles[J]. Physical Chemistry Chemical Physics, 2016, 18(8):5883-5895. doi: 10.1039/c5cp07709e pmid: 26841284
[19]	FU J, XU Z L. Accurate image-charge method by the use of the residue theorem for core-shell dielectric sphere[J]. The Journal of Chemical Physics, 2018, 148(5):054105.
[20]	马西奎. 电磁场理论及应用[M]. 西安: 西安交通大学出版社, 2000.
	MA X K. Theory and application of electromagnetic field[M]. Xi’an: Xi’an Jiaotong University Press, 2000.
[21]	WASHIZU M. Precise calculation of dielectrophoretic force in arbitrary field[J]. Journal of Electrostatics, 1993, 29(2):177-188.
[22]	MATSUYAMA T, YAMAMOTO H. Theelectrostatic force between a charged dielectric particle and a conducting plane [Translated][J]. KONA Powder and Particle Journal, 1998,16:223-228.
[23]	徐学基, 诸定昌. 气体放电物理[M]. 上海: 复旦大学出版社,1996.
	XU X J, ZHU D C. Gas discharge physics[M]. Shanghai: Fudan University Press,1996. (in Chinese)
[24]	GO D, VENKATTRAMAN A Microscale gas breakdown:ion-enhanced field emission and the modified Paschen’s curve[J]. Journal of Physics D:Applied Physics, 2014, 47(50):503001.
[25]	DANIELS D J, ROAD C. UWB radar for the detection of buried ordnance[R]. NATO/OTAN,unclassified/unlimited,ftp.rta.nato.int/public/PubFullText/RTO//MP-SET-120-KN doc, 2008.
[26]	李志敏. 起爆药静电响应规律与安全设计[D]. 北京: 北京理工大学, 2014.
	LI Z M. Theresponse law and safety designs of primary explosives to static electricity[D]. Beijing: Beijing Institute of Technology, 2014. (in Chinese)
[27]	XU Z. Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction[J]. Physical Review E, 2013, 87(1):013307.
[28]	XU C, ZHANG B B, WANG A C, et al. Effects of metal work function and contact potential difference on electron thermionic emission in contact electrification[J]. Advanced Functional Materials, 2019,29:1903142.
[29]	卫水爱. 发射药混同过程静电安全问题研究[D]. 北京: 北京理工大学, 2019.
	WEI S A. The research of electrostatic safety for gunpowder mixing[D]. Beijing: Beijing Institute of Technology, 2019. (in Chinese)