Electroosmotic Micro Thrusters of Phan-Thien-Tanner (PTT) Fluid at High Zeta Potential
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摘要: 在高的壁面zeta电势下, 考查了Phan-Thien-Tanner(PTT)黏弹性流体在平行板微通道中的电渗推进器问题. 在没有考虑Debye-Hückel线性近似的条件下, 求解了非线性Poisson-Boltzmann方程, 得到了高zeta电势下电势的解析解. 通过求解PTT流体满足的Cauchy动量方程, 获得了Navier滑移条件下微推进器速度的数值解. 进而通过数值积分得到了电渗微推进器的性能分布, 包括比冲、推力、效率和推力-功率比. 最后, 详细分析了黏弹性参数、壁面zeta电势、滑移系数和双电层厚度对速度分布及推进器性能的影响. 结果表明, 与Newton流体相比, PTT流体作为推进剂有利于推进器性能的提高, 比如, 流体速度随着黏弹性参数的增大而增大, 导致推进器性能也呈增大的趋势. 此外, 当前推进器比冲为800~1 000 ms时，推力可达0~250 μN, 效率为6%~12%, 推力-功率比为0~20 mN/W.Abstract: Electroosmotic micro thrusters filled with Phan-Thien-Tanner (PTT) viscoelastic fluid between 2 parallel plates were investigated at high wall zeta potential. The nonlinear Poisson-Boltzmann equation was solved without the Debye-Hückel linear approximation, to obtain the analytical electric potential at the high zeta potential. The numerical velocity of the micro thruster was given under the Navier slip condition in solution of the Cauchy momentum equation satisfied by the PTT fluid. Performances of the micro thrusters, including the specific impulse, the thrust, the efficiency, and the thrust-to-power ratio, were obtained through numerical integration. Finally, effects of the viscoelastic parameters, the wall zeta potential, the slip coefficient, and the double electric layer thickness on the velocity distributions and propeller performances, were discussed. The results show that, compared with the Newtonian fluid, the PTT fluid as a propellant is conducive to the improvement of propeller performances. For example, the fluid velocity increases with the viscoelastic parameters, resulting in an increasing trend of propeller performances. The present thruster delivers a thrust about 0~250 μN with a specific impulse of 800~1 000 ms, achieving an efficiency of 6%~12% and a thrust-power ratio of 0~20 mN/W.
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Key words:
- high zeta potential /
- electroosmotic flow /
- micro-thruster /
- thruster performance
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图 1 平行板微管道中黏弹性流体的纯电渗流
Figure 1. The pure electroosmotic flow of the viscoelastic fluid in a parallel plate microchannel
图 3 对于不同的εDe2, 电渗微推进器的速度分布
Figure 3. The velocity distributions of the electroosmotic microthruster for different values of εDe2
图 4 对于不同的εDe2值, 推进器性能随κ的变化情况
Figure 4. The thruster performance changes with κ for different values of εDe2
图 5 在不同的zeta电势下, 电渗微推进器的速度分布
Figure 5. The velocity distributions of the electroosmotic microthruster for different zeta values
图 6 在不同zeta电势下, 推进器性能随κ的变化情况
Figure 6. The thruster performance changes with κ for different zeta values
图 7 当滑移系数knl取不同值时, 电渗微推进器的速度分布
Figure 7. The velocity distributions of the electroosmotic microthruster for different slip coefficients
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[1] SMITH R S, HADAEGH F Y. Control of deep-space formation-flying spacecraft; relative sensing and switched information[J]. Journal of Guidance, Control, and Dynamics, 2005, 28(1): 106-114. doi: 10.2514/1.6165 [2] 徐晓辉. 深空探测中的微型推进器技术[J]. 机电产品开发与创新, 2007, 20(6): 29-31. https://www.cnki.com.cn/Article/CJFDTOTAL-JDCP200706013.htmXU Xiaohui. Micro thruster technology in deep-space exploring[J]. Development & Innovation of Machinery & Electrical Products, 2007, 20(6): 29-31. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JDCP200706013.htm [3] BLANCO A, ROY S. Rarefied gas electro jet (RGEJ) micro-thruster for space propulsion[J]. Journal of Physics D: Applied Physics, 2017, 50(45): 455201. doi: 10.1088/1361-6463/aa8c47 [4] MARTINEZ-SANCHEZ M, POLLARD J E. Spacecraft electric propulsion-an overview[J]. Journal of Propulsion and Power, 1998, 14(5): 688-699. doi: 10.2514/2.5331 [5] TAKAHASHI T, TAKAO Y, ERIGUCHI K, et al. Microwave-excited microplasma thruster: a numerical and experimental study of the plasma generation and micronozzle flow[J]. Journal of Physics D: Applied Physics, 2008, 41(19): 194005. doi: 10.1088/0022-3727/41/19/194005 [6] KEIDAR M, ZHUANG T, SHASHURIN A, et al. Electric propulsion for small satellites[J]. Plasma Physics and Controlled Fusion, 2014, 57(1): 014005. [7] 朴思扬, 朱春艳, 褚福运, 等. 基于等效梁模型的运载火箭动力学特性仿真预示研究[J]. 应用数学和力学, 2020, 41(3): 280-291. doi: 10.21656/1000-0887.400256PIAO Siyang, ZHU Chunyan, CHU Fuyun, et al. Dynamic characteristics prediction of launch vehicles based on the equivalent beam model[J]. Applied Mathematics and Mechanics, 2020, 41(3): 280-291. (in Chinese) doi: 10.21656/1000-0887.400256 [8] LYKLEMA J. Fundamentals of Interface and Colloid Science: Soft Colloids[M]. Elsevier, 2005. [9] QIAO R. Control of electroosmotic flow by polymer coating: effects of the electrical double layer[J]. Langmuir, 2006, 22(16): 7096-7100. doi: 10.1021/la060883t [10] 解智勇. 两层微流体系统中的电动流动及传热分析[D]. 博士学位论文. 呼和浩特: 内蒙古大学, 2019.XIE Zhiyong. The analysis of electrokinetic flow and heat transfer characteristic through a two-layer microfluidic system[D]. PhD Thesis. Hohhot: Inner Mongolia University, 2019. (in Chinese) [11] 罗艳, 李鸣, 杨大勇. 微通道内电渗压力混合驱动幂律流体流动模拟[J]. 应用数学和力学, 2016, 37(4): 373-381. doi: 10.3879/j.issn.1000-0887.2016.04.005LUO Yan, LI Ming, YANG Dayong. Simulation of mixed electroosmotic and pressure-driven flows of power-law fluids in microchannels[J]. Applied Mathematics and Mechanics, 2016, 37(4): 373-381. (in Chinese) doi: 10.3879/j.issn.1000-0887.2016.04.005 [12] 王爽, 菅永军. 周期壁面电势调制下平行板微管道中的电磁电渗流动[J]. 应用数学和力学, 2020, 41(4): 396-405. doi: 10.21656/1000-0887.400151WANG Shuang, JIAN Yongjun. Magnetohydrodynamic electroosmotic flow in zeta potential patterned micro-parallel channels[J]. Applied Mathematics and Mechanics, 2020, 41(4): 396-405. (in Chinese) doi: 10.21656/1000-0887.400151 [13] 张凯, 林建忠, 李志华. 电渗驱动微通道流中的扩散[J]. 应用数学和力学, 2006, 27(5): 512-518. http://www.applmathmech.cn/article/id/714ZHANG Kai, LIN Jianzhong, LI Zhihua. Diffusion in the micro-channel flow driven by electroosmosis[J]. Applied Mathematics and Mechanics, 2006, 27(5): 512-518. (in Chinese) http://www.applmathmech.cn/article/id/714 [14] JI J, QIAN S, LIU Z. Electroosmotic flow of viscoelastic fluid through a constriction microchannel[J]. Micromachines, 2021, 12(4): 417. doi: 10.3390/mi12040417 [15] MARTÍNEZ L, BAUTISTA O, ESCANDÓN J, et al. Electroosmotic flow of a Phan-Thien-Tanner fluid in a wavy-wall microchannel[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2016, 498: 7-19. [16] DIEZ F J, HERNAIZ G, MIRANDA J J, et al. On the capabilities of nano electrokinetic thrusters for space propulsion[J]. Acta Astronautica, 2013, 83: 97-107. doi: 10.1016/j.actaastro.2012.09.020 [17] HUANG K H, HUANG H F. Two-liquid electroosmotic thrusters for micro propulsion applications[J]. Physics of Fluids, 2019, 31(12): 122003. doi: 10.1063/1.5128274 [18] ZHENG J, JIAN Y. Electroosmotic thrusters in soft nanochannels for space propulsion[J]. Physics of Fluids, 2020, 32(12): 122005. doi: 10.1063/5.0033436 [19] ZHENG J, JIAN Y. Space electroosmotic thrusters in ion partitioning soft nanochannels[J]. Micromachines, 2021, 12: 777. doi: 10.3390/mi12070777 [20] ZHENG J, JIA B, JIAN Y. Steric effects on space electroosmotic thrusters in soft nanochannels[J]. Mathematics, 2021, 9(16): 1916. doi: 10.3390/math9161916 [21] PHAN-THIEN N, TANNER R I. A new constitutive equation derived from network theory[J]. Journal of Non-Newtonian Fluid Mechanics, 1977, 93(2/3): 353-365. [22] OLIVEIRA P J, PINHO F T. Analytical solution for fully developed channel and pipe flow of Phan-Thien-Tanner fluids[J]. Journal of Non-Newtonian Fluid Mechanics, 1999, 387: 271-280. http://web.fe.up.pt/~fpinho/pdfs/jfma.pdf [23] PINHO F T, OLIVEIRA P J. Analysis of forced convection in pipes and channels with the simplified Phan-Thien-Tanner fluid[J]. International Journal of Heat and Mass Transfer, 2000, 43(13): 2273-2287. doi: 10.1016/S0017-9310(99)00303-8 [24] PINHO F T, OLIVEIRA P J. Axial annular flow of a nonlinear viscoelastic fluid: an analytical solution[J]. Journal of Non-Newtonian Fluid Mechanics, 2000, 93(2/3): 325-337. [25] CRUZ D O A, PINHO F T. Skewed Poiseuille-Couette flows of sPTT fluids in concentric annuli and channels[J]. Journal of Non-Newtonian Fluid Mechanics, 2004, 121(1): 1-14. doi: 10.1016/j.jnnfm.2004.03.007 [26] 许晓阳, 彭严, 邓方安. 三维PTT黏弹性液滴撞击固壁面问题的改进SPH模拟[J]. 应用数学和力学, 2015, 36(6): 616-627. doi: 10.3879/j.issn.1000-0887.2015.06.006XU Xiaoyang, PENG Yan, DENG Fang'an. Numerical simulation of 3D PTT droplet impact onto solid surface with an improved smoothed particle hydrodynamics method[J]. Applied Mathematics and Mechanics, 2015, 36(6): 616-627. (in Chinese) doi: 10.3879/j.issn.1000-0887.2015.06.006 [27] HASHEMABADI S H, ETEMAD S G, THIBAULT J, et al. Analytical solution for dynamic pressurization of viscoelastic fluids[J]. International Journal of Heat and Fluid Flow, 2003, 24(1): 137-144. doi: 10.1016/S0142-727X(02)00204-7 [28] FERRÁS L L, AFONSO A M, ALVES M A, et al. Annular flow of viscoelastic fluids: analytical and numerical solutions[J]. Journal of Non-Newtonian Fluid Mechanics, 2014, 212: 80-91. doi: 10.1016/j.jnnfm.2014.07.004 [29] SARMA R, DEKA N, SARMA K, et al. Electroosmotic flow of Phan-Thien-Tanner fluids at high zeta potentials: an exact analytical solution[J]. Physics of Fluids, 2018, 30(6): 062001. doi: 10.1063/1.5033974 [30] PARDON G, VAN DER WIJNGAART W. Modeling and simulation of electrostatically gated nanochannels[J]. Advances in Colloid and Interface Science, 2013, 199/200: 78-94. doi: 10.1016/j.cis.2013.06.006 [31] FERRÁS L L, AFONSO A M, ALVES M A, et al. Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: analytical and semi-analytical solutions[J]. Physics of Fluids, 2016, 28(9): 093102. doi: 10.1063/1.4962357 [32] ANAND V. Effect of slip on heat transfer and entropy generation characteristics of simplified Phan-Thien-Tanner fluids with viscous dissipation under uniform heat flux boundary conditions: exponential formulation[J]. Applied Thermal Engineering, 2016, 98: 455-473. doi: 10.1016/j.applthermaleng.2015.12.025 [33] BRUUS H. Theoretical Microfluidics[M]. Oxford: Oxford University Press, 2008. [34] PHAN-THIEN N. A nonlinear network viscoelastic model[J]. Journal of Rheology, 1978, 22(3): 259-283. doi: 10.1122/1.549481 [35] FERRÁS L L, NÓBREGA J M, PINHO F T. Analytical solutions for channel flows of Phan-Thien-Tanner and Giesekus fluids under slip[J]. Journal of Non-Newtonian Fluid Mechanics, 2012, 171: 97-105. [36] SMOLUCHOWSKI M. Versuch einer mathematischen theorie der koagulationskinetik kolloider lösungen[J]. Zeitschrift für Physikalische Chemie, 1918, 92(1): 129-168. [37] PARK H M, LEE W M. Helmholtz-Smoluchowski velocity for viscoelastic electroosmotic flows[J]. Journal of Colloid and Interface Science, 2008, 317(2): 631-636. doi: 10.1016/j.jcis.2007.09.027 [38] PROBSTEIN R F. Physicochemical Hydrodynamics[M]. Wiley Interscience, 2003. [39] EIJKEL J C T. Liquid slip in micro- and nanofluidics: recent research and its possible implications[J]. Lab on a Chip, 2007, 7(3): 299-301. doi: 10.1039/b700364c [40] SCHOWALTER W R. The behavior of complex fluids at solid boundaries[J]. Journal of Non-Newtonian Fluid Mechanics, 1988, 29: 25-36. doi: 10.1016/0377-0257(88)85048-1 [41] NAVIER C. Mémoire sur les lois du mouvement des fluides[J]. Mémoires de l'Académie Royale des Sciences de l'Institut de France, 1823, 6(1823): 389-440. [42] FERNANDES C, FERRÁS L L, HABLA F, et al. Implementation of partial slip boundary conditions in an open-source finite-volume-based computational library[J]. Journal of Polymer Engineering, 2019, 39(4): 377-387. [43] 张雪儿, 李得天, 张天平. 电推进三种比冲的定义及其工程应用[J]. 真空与低温, 2020, 26(6): 486-493. https://www.cnki.com.cn/Article/CJFDTOTAL-ZKDW202006011.htmZHANG Xueer, LI Detian, ZHANG Tianping. Three types of specific impulses for electric propulsions: their definitions and engineering applications[J]. Vacuum & Cryogenics, 2020, 26(6): 486-493. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZKDW202006011.htm [44] GOEBEL D M, KATZ I. Fundamentals of Electric Propulsion: Ion and Hall Thrusters[M]. John Wiley & Sons, 2008. [45] HEY F G. Micro Newton Thruster Development: Direct Thrust Measurements and Thruster Downscaling[M]. Springer, 2018. [46] JONCQUIERES V, VERMOREL O, CUENOT B. A fluid formalism for low-temperature plasma flows dedicated to space propulsion in an unstructured high performance computing solver[J]. Plasma Sources Science and Technology, 2020, 29(9): 095005. [47] ESCANDÓN J P, BAUTISTA O, MÉNDEZ F, et al. Theoretical conjugate heat transfer analysis in a parallel flat plate microchannel under electro-osmotic and pressure forces with a Phan-Thien-Tanner fluid[J]. International Journal of Thermal Sciences, 2011, 50(6): 1022-1030. [48] ESCANDÓN J, SANTIAGO F, BAUTISTA O, et al. Hydrodynamics and thermal analysis of a mixed electromagnetohydrodynamic-pressure driven flow for Phan-Thien-Tanner fluids in a microchannel[J]. International Journal of Thermal Sciences, 2014, 86: 246-257. [49] DHINAKARAN S, AFONSO A M, ALVES M A, et al. Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan-Thien-Tanner model[J]. Journal of Colloid and Interface Science, 2010, 344(2): 513-520. -
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