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Studies of the driving force of the self-propulsion Janus particles are very important in the fields of micro-power and nano-motor. In this paper, we choose the micron Pt-SiO2-type Janus particle as a research object, which is propelled by self-generated concentration gradient in the dilute solution of H2O2, focusing on the self-propulsion of the single particle. According to the force analysis of the Janus particle, the surface force can be decomposed into the viscous resistance of the fluid, the Brownian force derived from the molecular thermal fluctuation, and the diffusiophoresis caused by the diffusion of the solute component. The main aim of this paper is to find the way to accurately simulate the diffusiophoresis generated by the huge concentration gradient on a microscale. The lattice Boltzmann method (LBM) is a modern mesoscopic method based on the microscopic particle characteristics of the fluid, which makes it more intuitive to deal with the interaction between the fluid and solid. It is more advantageous than the traditional numerical method in the description of this micro-interface dynamic problem, i.e., the self-propulsion of Janus particle. On a certain time scale, when the Janus particle shows the directional motion, the influence of the Brownian force can be ignored. Thus, the analytical process can be simplified. Based on the momentum theorem, the method of calculating the diffusiophoresis produced by concentration diffusion is proposed. We introduce the momentum exchange in the half-way bounce-back scheme of LBM into the model of the multicomponent diffusion and reaction. Through counting the surface force we can obtain the diffusiophoresis acting on the Janus particle. Moreover, this diffusiophoresis model is modified by comparing the experimental fluid resistance with simulated one. This comparision verifies the validity of the diffusiophoresis model. Then, the analysis of the variation of diffusiophoresis proves that the value of diffusiophoresis is independent of the fluid velocity. Through the further application of this model, the different shapes of Janus particles with the same volume are compared in simulations. The results show that the self-diffusiophoresis is mainly determined by the axial projection area. In addition, the reaction area of the particle also affects the value of the diffusiophoresis.
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Keywords:
- lattice Boltzmann method /
- Janus particles /
- numerical simulation /
- diffusiophoresis
[1] Zhao Y P 2012 Physical Mechanics of Surfaces and Interfaces (Beijing: Science Press) p399 (in Chinese) [赵亚溥 2012 表面与界物理力学 (北京: 科学版社) 第 399 页]
[2] Soong R K, Bachand G D, Neves H P, Olkhovets A G, Craighead H G, Montemagno C D 2000 Science 290 1555
[3] Wang W, Duan W, Ahmed S, Mallouk T E, Sen A 2013 Nano Today 8 531
[4] Jiang S, Granick S, Schneider H J 2012 Janus Particle Synthesis, Self Assembly and Applications (USA: RSC Publishing Press) pp1-25
[5] Chernyak V G, Starikov S A, Beresnev S A 2001 J. Appl. Mech. Tech. Phys. 42 445
[6] Patra D, Sengupta S, Duan W, Zhang H, Pavlick R, Sen A 2013 Nanoscale 5 1273
[7] Rckner G, Kapral R 2007 Phys. Rev. Lett. 98 150603
[8] Howse J R, Jones R A, Ryan A J, Gough T, Vafabakhsh R, Golestanian R 2007 Phys. Rev. Lett. 99 048102
[9] Ke H, Ye S, Carroll R L, Showalter K 2010 J. Phys. Chem. A 114 5462
[10] Zheng X, Hagen B T, Kaiser A, Wu M, Cui H H, Silber-Li Z, Lwen H 2013 Phys. Rev. E 88 032304
[11] Gong C L 2013 M. S. Thesis ( Xian: Xi'an University of Architecture and Technology) (in Chinese) [宫春亮 2013 硕士学位论文 (西安: 西安建筑科技大学)]
[12] Crdova-Figueroa U M, Brady J F 2008 Phys. Rev. Lett. 100 158303
[13] de Buyl P, Kapral R 2013 Nanoscale 5 1337
[14] Hu J, Zhang H Y, Zheng X, Cui H H 2014 Chinese J. Hydrodynamics 04 377 (in Chinese) [胡静, 张鸿雁, 郑旭, 崔海航 2014 水动力学研究与进展 04 377]
[15] Cui H H, Tan X J, Zhang H Y 2014 Nanotechnology and Precision Engineering 12 340 (in Chinese) [崔海航, 谭晓君, 张鸿雁 2014 纳米技术与精密工程 12 340]
[16] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing: Science Press) p10 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann 方法的原理及应用(北京: 科学出版社) 第 10 页]
[17] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[18] Shan X, Doolen G 1995 J. Stat. Phys. 81 379
[19] Zhang R L, Di Q W, Wang X L, Ding W P, Gong W 2012 Mechanics in Engineering 2 10 (in Chinese) [张任良, 狄勤丰, 王新亮, 丁伟朋, 龚玮 2012 力学与实践 2 10]
[20] Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 07403 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]
[21] Wang L L, Cui H H, Zhang J, Zheng X, Wang L, Chen L 2016 Acta Phys. Sin. 65 220201 (in Chinese) [王雷磊, 崔海航, 张静, 郑旭, 王磊, 陈力 2016 物理学报 65 220201]
[22] Wu M L 2014 M. S. Thesis (Xi'an: Xi'an University of Architecture and Technology) (in Chinese) [武美玲 2014 硕士学位论文 (西安: 西安建筑科技大学)]
[23] Cui H H, Tan X J, Zhang H Y, Chen L 2015 Acta Phys. Sin. 64 134705 (in Chinese) [崔海航, 谭晓君, 张鸿雁, 陈力 2015 物理学报 64 134705]
[24] Casson V, Maschio G 2011 Ind. Eng. Chem. Res. 51 7526
[25] Ladd A J C 1994 J. Fluid Mech. 271 285
[26] Ladd A J C 1994 J. Fluid Mech. 271 311
[27] Zhang T 2001 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [张婷 2012 博士学位论文 (武汉: 华中科技大学)]
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[1] Zhao Y P 2012 Physical Mechanics of Surfaces and Interfaces (Beijing: Science Press) p399 (in Chinese) [赵亚溥 2012 表面与界物理力学 (北京: 科学版社) 第 399 页]
[2] Soong R K, Bachand G D, Neves H P, Olkhovets A G, Craighead H G, Montemagno C D 2000 Science 290 1555
[3] Wang W, Duan W, Ahmed S, Mallouk T E, Sen A 2013 Nano Today 8 531
[4] Jiang S, Granick S, Schneider H J 2012 Janus Particle Synthesis, Self Assembly and Applications (USA: RSC Publishing Press) pp1-25
[5] Chernyak V G, Starikov S A, Beresnev S A 2001 J. Appl. Mech. Tech. Phys. 42 445
[6] Patra D, Sengupta S, Duan W, Zhang H, Pavlick R, Sen A 2013 Nanoscale 5 1273
[7] Rckner G, Kapral R 2007 Phys. Rev. Lett. 98 150603
[8] Howse J R, Jones R A, Ryan A J, Gough T, Vafabakhsh R, Golestanian R 2007 Phys. Rev. Lett. 99 048102
[9] Ke H, Ye S, Carroll R L, Showalter K 2010 J. Phys. Chem. A 114 5462
[10] Zheng X, Hagen B T, Kaiser A, Wu M, Cui H H, Silber-Li Z, Lwen H 2013 Phys. Rev. E 88 032304
[11] Gong C L 2013 M. S. Thesis ( Xian: Xi'an University of Architecture and Technology) (in Chinese) [宫春亮 2013 硕士学位论文 (西安: 西安建筑科技大学)]
[12] Crdova-Figueroa U M, Brady J F 2008 Phys. Rev. Lett. 100 158303
[13] de Buyl P, Kapral R 2013 Nanoscale 5 1337
[14] Hu J, Zhang H Y, Zheng X, Cui H H 2014 Chinese J. Hydrodynamics 04 377 (in Chinese) [胡静, 张鸿雁, 郑旭, 崔海航 2014 水动力学研究与进展 04 377]
[15] Cui H H, Tan X J, Zhang H Y 2014 Nanotechnology and Precision Engineering 12 340 (in Chinese) [崔海航, 谭晓君, 张鸿雁 2014 纳米技术与精密工程 12 340]
[16] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing: Science Press) p10 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann 方法的原理及应用(北京: 科学出版社) 第 10 页]
[17] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[18] Shan X, Doolen G 1995 J. Stat. Phys. 81 379
[19] Zhang R L, Di Q W, Wang X L, Ding W P, Gong W 2012 Mechanics in Engineering 2 10 (in Chinese) [张任良, 狄勤丰, 王新亮, 丁伟朋, 龚玮 2012 力学与实践 2 10]
[20] Shi D Y, Wang Z K, Zhang A M 2014 Acta Phys. Sin. 63 07403 (in Chinese) [史冬岩, 王志凯, 张阿漫 2014 物理学报 63 074703]
[21] Wang L L, Cui H H, Zhang J, Zheng X, Wang L, Chen L 2016 Acta Phys. Sin. 65 220201 (in Chinese) [王雷磊, 崔海航, 张静, 郑旭, 王磊, 陈力 2016 物理学报 65 220201]
[22] Wu M L 2014 M. S. Thesis (Xi'an: Xi'an University of Architecture and Technology) (in Chinese) [武美玲 2014 硕士学位论文 (西安: 西安建筑科技大学)]
[23] Cui H H, Tan X J, Zhang H Y, Chen L 2015 Acta Phys. Sin. 64 134705 (in Chinese) [崔海航, 谭晓君, 张鸿雁, 陈力 2015 物理学报 64 134705]
[24] Casson V, Maschio G 2011 Ind. Eng. Chem. Res. 51 7526
[25] Ladd A J C 1994 J. Fluid Mech. 271 285
[26] Ladd A J C 1994 J. Fluid Mech. 271 311
[27] Zhang T 2001 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese) [张婷 2012 博士学位论文 (武汉: 华中科技大学)]
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