Skip to main content
SpringerLink
Log in

Dynamic self-assembly of staggered oblate particle train in a square duct

交错扁球颗粒链在方形管道中的动态自组装行为

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

The dynamic self-assembly of staggered oblate particle train in a three-dimensional square duct is numerically investigated via the multiple-relaxation-time lattice Boltzmann method. The present study aims to explore the effect of the Reynolds number (Re), average length fraction (〈Lf〉), and particle aspect ratio (AR) on the entire migration process, distribution pattern, and mean axial interparticle spacing (di/D)uni. Herein, it should be noted that AR is varied by changing the polar radius of the oblate particle, whereas the corresponding equatorial radius, i.e., the rotational diameter, keeps unchanged. The whole forming process of the staggered oblate particle train consists of the inertial migration toward the face equilibrium positions and the dynamic self-assembly in the streamwise direction. Present results indicate that the distribution pattern and (di/D)uni of the staggered oblate particle train are significantly dependent on 〈Lf〉 and Re. Within the parameter range studied, continuous pattern, with all inter-particle distances being identical, preferentially appears in high 〈Lf〉 and large Re for moderate 〈Lf〉. As 〈Lf〉 increases, the corresponding (di/D)uni ≈ 1/〈Lf〉 decreases. Discontinuous pattern, with varying inter-particle distances, occurs in low 〈Lf〉 and small Re for moderate 〈Lf〉, where (di/D)uni is mainly determined by Re. The data show that (di/D)uni increases linearly with Re. Furthermore, at 〈Lf〉 = 0.4, particles with AR = 0.5, 0.75, 1 all self-organize into staggered train with the discontinuous pattern for Re ≤ 40 with a non-monotonic dependence of (di/D)uni on AR, while they are in the continuous pattern for Re ≥ 60. Nevertheless, due to the same rotational diameter, particles with different AR yield almost the same face equilibrium positions.

摘要

本文采用多松弛格子Boltzmann模型数值研究了三维方管中交错排列的扁球颗粒的动态自组装行为, 着重考虑了雷诺数(Re)、 平均长度分数(⟨Lf ⟩)和颗粒纵横比(AR)对整个迁移过程、分布模态和平均轴向颗粒间距(di/D)uni的影响. 这里颗粒AR是通过改变扁球 颗粒的极轴半径来调节, 相应的赤道半径保持不变. 交错扁球颗粒链的整个形成过程包括向平衡位置的惯性迁移和在流向方向上的动 态自组装行为. 目前结果表明分布模态和交错扁球颗粒链的(di/D)uni明显依赖于⟨Lf ⟩和Re. 在当前研究的参数范围内, 在中等⟨Lf ⟩下 高Re或高⟨Lf ⟩时, 颗粒链呈现连续模态. 此时, 所有轴向颗粒间距达到相同的值. 随着⟨Lf ⟩增加, 相应的(di/D)uni减少. 在中等⟨Lf ⟩下 小Re或低⟨Lf ⟩时, 颗粒链呈现间断模态. 此模态下, (di/D)uni主要随Re线性增加. 此外, 当⟨Lf ⟩ = 0.4时, AR从0.5 变成0.75或1 不会改 变颗粒链的模态, 即Re ≤ 40时为间断模态, 而Re ≥ 60时为连续模态. 在间断模态下, (di/D)uni对AR并没有体现出明显的线性依赖关系. 由于旋转直径相同, 相同Re下颗粒链的面平衡位置几乎不受AR的影响.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. Segré, and A. Silberberg, Radial particle displacements in Poiseuille flow of suspensions, Nature 189, 209 (1961).

    Article  Google Scholar 

  2. G. Segré, and A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow, Part 2. Experimental results and interpretation, J. Fluid Mech. 14, 136 (1962).

    Article  MATH  Google Scholar 

  3. B. P. Ho, and L. G. Leal, Migration of rigid spheres in a two-dimensional unidirectional shear flow of a second-order fluid, J. Fluid Mech. 76, 783 (1976).

    Article  MATH  Google Scholar 

  4. K. Hood, S. Lee, and M. Roper, Inertial migration of a rigid sphere in three-dimensional Poiseuille flow, J. Fluid Mech. 765, 452 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Chun, and A. J. C. Ladd, Inertial migration of neutrally buoyant particles in a square duct: An investigation of multiple equilibrium positions, Phys. Fluids 18, 031704 (2006).

    Article  Google Scholar 

  6. I. Lashgari, M. N. Ardekani, I. Banerjee, A. Russom, and L. Brandt, Inertial migration of spherical and oblate particles in straight ducts, J. Fluid Mech. 819, 540 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Su, X. Chen, and G. Hu, Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters, Phys. Fluids 30, 032007 (2018).

    Article  Google Scholar 

  8. X. Hu, J. Lin, D. Chen, and X. Ku, Influence of non-Newtonian power law rheology on inertial migration of particles in channel flow, Biomicrofluidics 14, 014105 (2020).

    Article  Google Scholar 

  9. H. Yamashita, T. Itano, and M. Sugihara-Seki, Bifurcation phenomena on the inertial focusing of a neutrally buoyant spherical particle suspended in square duct flows, Phys. Rev. Fluids 4, 124307 (2019).

    Article  Google Scholar 

  10. J. P. Matas, J. F. Morris, and É. Guazzelli, Inertial migration of rigid spherical particles in Poiseuille flow, J. Fluid Mech. 515, 171 (2004).

    Article  MATH  Google Scholar 

  11. D. Di Carlo, J. F. Edd, K. J. Humphry, H. A. Stone, and M. Toner, Particle segregation and dynamics in confined flows, Phys. Rev. Lett. 102, 094503 (2009).

    Article  Google Scholar 

  12. Y. S. Choi, K. W. Seo, and S. J. Lee, Lateral and cross-lateral focusing of spherical particles in a square microchannel, Lab Chip 11, 460 (2011).

    Article  Google Scholar 

  13. M. Abbas, P. Magaud, Y. Gao, and S. Geoffroy, Migration of finite sized particles in a laminar square channel flow from low to high Reynolds numbers, Phys. Fluids 26, 123301 (2014).

    Article  Google Scholar 

  14. Y. Gao, P. Magaud, L. Baldas, C. Lafforgue, M. Abbas, and S. Colin, Self-ordered particle trains in inertial microchannel flows, Microfluid Nanofluid 21, 154 (2017).

    Article  Google Scholar 

  15. Y. Gao, P. Magaud, C. Lafforgue, S. Colin, and L. Baldas, Inertial lateral migration and self-assembly of particles in bidisperse suspensions in microchannel flows, Microfluid Nanofluid 23, 93 (2019).

    Article  Google Scholar 

  16. C. Yuan, Z. Pan, and H. Wu, Inertial migration of single particle in a square microchannel over wide ranges of Re and particle sizes, Microfluid Nanofluid 22, 1 (2018).

    Article  Google Scholar 

  17. K. Miura, T. Itano, and M. Sugihara-Seki, Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels, J. Fluid Mech. 749, 320 (2014).

    Article  Google Scholar 

  18. Y. Li, Z. Xia, and L. P. Wang, Inertial migration of a neutrally buoyant oblate spheroid in three-dimensional square duct poiseuille flows, Int. J. Multiphase Flow 155, 104148 (2022).

    Article  MathSciNet  Google Scholar 

  19. H. Shichi, H. Yamashita, J. Seki, T. Itano, and M. Sugihara-Seki, Inertial migration regimes of spherical particles suspended in square tube flows, Phys. Rev. Fluids 2, 044201 (2017).

    Article  Google Scholar 

  20. J. P. Matas, V. Glezer, É. Guazzelli, and J. F. Morris, Trains of particles in finite-Reynolds-number pipe flow, Phys. Fluids 16, 4192 (2004).

    Article  MATH  Google Scholar 

  21. J. M. Martel, and M. Toner, Inertial focusing in microfluidics, Annu. Rev. Biomed. Eng. 16, 371 (2014).

    Article  Google Scholar 

  22. Z. Li, and J. Lin, On the some issues of particle motion in the flow of viscoelastic fluids, Acta Mech. Sin. 38, 321467 (2022).

    Article  Google Scholar 

  23. S. C. Hur, H. T. K. Tse, and D. Di Carlo, Sheathless inertial cell ordering for extreme throughput flow cytometry, Lab Chip 10, 274 (2010).

    Article  Google Scholar 

  24. J. F. Edd, D. Di Carlo, K. J. Humphry, S. Köster, D. Irimia, D. A. Weitz, and M. Toner, Controlled encapsulation of single-cells into monodisperse picolitre drops, Lab Chip 8, 1262 (2008).

    Article  Google Scholar 

  25. F. Del Giudice, G. D’Avino, and P. L. Maffettone, Microfluidic formation of crystal-like structures, Lab Chip 21, 2069 (2021).

    Article  Google Scholar 

  26. D. Di Carlo, D. Irimia, R. G. Tompkins, and M. Toner, Continuous inertial focusing, ordering, and separation of particles in microchannels, Proc. Natl. Acad. Sci. USA 104, 18892 (2007).

    Article  Google Scholar 

  27. W. Lee, H. Amini, H. A. Stone, and D. Di Carlo, Dynamic self-assembly and control of microfluidic particle crystals, Proc. Natl. Acad. Sci. USA 107, 22413 (2010).

    Article  Google Scholar 

  28. K. J. Humphry, P. M. Kulkarni, D. A. Weitz, J. F. Morris, and H. A. Stone, Axial and lateral particle ordering in finite Reynolds number channel flows, Phys. Fluids 22, 081703 (2010).

    Article  Google Scholar 

  29. S. Kahkeshani, H. Haddadi, and D. Di Carlo, Preferred interparticle spacings in trains of particles in inertial microchannel flows, J. Fluid Mech. 786, R3 (2016).

    Article  Google Scholar 

  30. Z. Pan, R. Zhang, C. Yuan, and H. Wu, Direct measurement of microscale flow structures induced by inertial focusing of single particle and particle trains in a confined microchannel, Phys. Fluids 30, 102005 (2018).

    Article  Google Scholar 

  31. A. Gupta, P. Magaud, C. Lafforgue, and M. Abbas, Conditional stability of particle alignment in finite-Reynolds-number channel flow, Phys. Rev. Fluids 3, 114302 (2018).

    Article  Google Scholar 

  32. X. Hu, J. Lin, and X. Ku, Inertial migration of circular particles in Poiseuille flow of a power-law fluid, Phys. Fluids 31, 073306 (2019).

    Article  Google Scholar 

  33. X. Hu, J. Lin, D. Chen, and X. Ku, Stability condition of self-organizing staggered particle trains in channel flow, Microfluid Nanofluid 24, 25 (2020).

    Article  Google Scholar 

  34. C. Schaaf, and H. Stark, Particle pairs and trains in inertial microfluidics, Eur. Phys. J. E 43, 1 (2020).

    Article  Google Scholar 

  35. J. Liu, H. Liu, and Z. Pan, Numerical investigation on the forming and ordering of staggered particle train in a square microchannel, Phys. Fluids 33, 073301 (2021).

    Article  Google Scholar 

  36. J. Liu, and Z. Pan, Self-ordering and organization of in-line particle chain in a square microchannel, Phys. Fluids 34, 023309 (2022).

    Article  Google Scholar 

  37. W. Mao, and A. Alexeev, Motion of spheroid particles in shear flow with inertia, J. Fluid Mech. 749, 145 (2014).

    Article  Google Scholar 

  38. T. Rosén, M. Do-Quang, C. K. Aidun, and F. Lundell, The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia, J. Fluid Mech. 771, 115 (2015).

    Article  Google Scholar 

  39. S. C. Hur, S. E. Choi, S. Kwon, and D. D. Carlo, Inertial focusing of non-spherical microparticles, Appl. Phys. Lett. 99, 044101 (2011).

    Article  Google Scholar 

  40. X. Hu, J. Lin, Y. Guo, and X. Ku, Motion and equilibrium position of elliptical and rectangular particles in a channel flow of a power-law fluid, Powder Tech. 377, 585 (2021).

    Article  Google Scholar 

  41. H. Huang, and X. Y. Lu, An ellipsoidal particle in tube Poiseuille flow, J. Fluid Mech. 822, 664 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  42. M. Masaeli, E. Sollier, H. Amini, W. Mao, K. Camacho, N. Doshi, S. Mitragotri, A. Alexeev, and D. Di Carlo, Continuous inertial focusing and separation of particles by shape, Phys. Rev. X 2, 031017 (2012).

    Google Scholar 

  43. X. Yang, H. Huang, and X. Lu, The motion of a neutrally buoyant ellipsoid inside square tube flows, Adv. Appl. Math. Mech. 9, 233 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  44. Y. Cui, X. Chang, and H. Huang, Experimental study of an ellipsoidal particle in tube Poiseuille flow, J. Hydrodyn. 32, 616 (2020).

    Article  Google Scholar 

  45. X. Hu, J. Lin, Y. Guo, and X. Ku, Inertial focusing of elliptical particles and formation of self-organizing trains in a channel flow, Phys. Fluids 33, 013310 (2021).

    Article  Google Scholar 

  46. P. F. Lin, X. Hu, and J. Z. Lin, Inertial focusing and rotating characteristics of elliptical and rectangular particle pairs in channel flow, Chin. Phys. B 31, 080501 (2022).

    Article  Google Scholar 

  47. H. Chen, S. Chen, and W. H. Matthaeus, Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method, Phys. Rev. A 45, R5339 (1992).

    Article  Google Scholar 

  48. Y. H. Qian, D. D’Humieres, and P. Lallemand, Lattice BGK models for Navier-Stokes equation, Europhys. Lett. 17, 479 (1992).

    Article  MATH  Google Scholar 

  49. S. Chen, and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30, 329 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  50. Z. Guo, C. Zheng, and B. Shi, Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys. Rev. E 65, 046308 (2002).

    Article  MATH  Google Scholar 

  51. D. d’Humiéres, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Phil. Trans. R. Soc. Lond. A. 360, 437 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  52. K. Suga, Y. Kuwata, K. Takashima, and R. Chikasue, A D3Q27 multiple-relaxation-time lattice Boltzmann method for turbulent flows, Comput. Math. Appl. 69, 518 (2015).

    MathSciNet  MATH  Google Scholar 

  53. C. Peng, N. Geneva, Z. Guo, and L. P. Wang, Direct numerical simulation of turbulent pipe flow using the lattice Boltzmann method, J. Comput. Phys. 357, 16 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  54. L. Li, Y. Shi, S. Zhang, L. P. Wang, and Z. Xia, On the comparison between lattice Boltzmann methods and spectral methods for DNS of incompressible turbulent channel flows on small domain size, Adv. Appl. Math. Mech. 11, 598 (2019).

    Article  MathSciNet  MATH  Google Scholar 

  55. D. Qi, Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows, J. Fluid Mech. 385, 41 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  56. M. Bouzidi, M. Firdaouss, and P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Phys. Fluids 13, 3452 (2001).

    Article  MATH  Google Scholar 

  57. A. J. C. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, J. Fluid Mech. 271, 285 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  58. Y. Chen, Q. Cai, Z. Xia, M. Wang, and S. Chen, Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions, Phys. Rev. E 88, 013303 (2013).

    Article  Google Scholar 

  59. B. Wen, C. Zhang, Y. Tu, C. Wang, and H. Fang, Galilean invariant fluid-solid interfacial dynamics in lattice Boltzmann simulations, J. Comput. Phys. 266, 161 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  60. D. Di Carlo, Inertial microfluidics, Lab Chip 9, 3038 (2009).

    Article  Google Scholar 

  61. Y. Li, H. Liang, and Z. Xia, Effect of neutrally buoyant oblate spheroid’s aspect ratio on its equilibrium position in a square duct, Sci. Sin.-Phys. Mech. Astron. 52, 104708 (2022).

    Article  Google Scholar 

  62. J. Feng, H. H. Hu, and D. D. Joseph, Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid, Part 1. Sedimentation, J. Fluid Mech. 261, 95 (1994).

    Article  MATH  Google Scholar 

  63. Z. Xia, K. W. Connington, S. Rapaka, P. Yue, J. J. Feng, and S. Chen, Flow patterns in the sedimentation of an elliptical particle, J. Fluid Mech. 625, 249 (2009).

    Article  MATH  Google Scholar 

  64. T. V. Nizkaya, A. S. Gekova, J. Harting, E. S. Asmolov, and O. I. Vinogradova, Inertial migration of oblate spheroids in a plane channel, Phys. Fluids 32, 112017 (2020).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 91852205).

Author information

Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems and Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China

    Yang Li  (李洋) & Zhenhua Xia  (夏振华)

  2. Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Lian-Ping Wang  (王连平)

Authors
  1. Yang Li  (李洋)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenhua Xia  (夏振华)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lian-Ping Wang  (王连平)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenhua Xia  (夏振华).

Additional information

Author contributions

Yang Li designed the research, carried out all the simulations and results analysis, wrote the first draft of the manuscript, and revised and edited the final version. Zhenhua Xia designed the research, offered methodology, computing resources and funding acquisition, and helped organize the manuscript, analyze the simulation results, and edit and revise the final version. Lian-Ping Wang offered methodology and funding acquisition, and helped organize the manuscript and revise the final version.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Xia, Z. & Wang, LP. Dynamic self-assembly of staggered oblate particle train in a square duct. Acta Mech. Sin. 39, 323006 (2023). https://doi.org/10.1007/s10409-023-23006-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-023-23006-x

Search

Navigation