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Colloidal hydrodynamics using a quasi-steady algorithm in lattice Boltzmann method

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Abstract

Hydrodynamics can play an important role in determining the behaviour of colloidal particles in many soft matter systems. Analytical solutions for fluid dynamics are limited and incorporating the particle dynamics in numerical methods is challenging, since grid points belonging to fluid and solid phases are exchanged during the simulations. As a solution, here, we introduce a quasi-steady method to simulate dynamics of particles within the frame work of lattice Boltzmann method. This method not only carries the advantages of lattice Boltzmann, namely the simple and straight forward algorithm of programming and the simplicity in imposing the boundary conditions, but it also avoids the complications associated with exchange of particle and fluid nodes. Exploiting the smallness of Reynold’s number associated with colloidal hydrodynamics, the proposed algorithm works in an instantaneous frame of reference and particle velocities are then calculated by imposing additional constraints of force and torque acting on the particle. We illustrate the method using the classic examples of settling particles and a system of recent interest-dynamics of active particles, both in the presence of a wall. Therefore, we expect the proposed method to be suitable and useful in variety of soft and active matter systems.

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References

  1. Jahn A, Vreeland W N, Gaitan M and Locasci L E 2004 J. Am. Chem. Soc. 126 2674

    Article  CAS  Google Scholar 

  2. Grzybowski B A and Whitesides G M 2002 J. Phys. Chem. B 106 1188

    Article  CAS  Google Scholar 

  3. Snezhko A and Aranson I S 2011 Nat. Mater. 10 698

    Article  CAS  Google Scholar 

  4. Sabouni R and Gomaa H G 2015 Colloids Surf. A: Physicochem. Eng. Asp. 484 416

    Article  CAS  Google Scholar 

  5. Gomaa H G and Sabouni R 2016 AIChE J. 62 2903

    Article  Google Scholar 

  6. Cosentino L M, Pagonabarraga I and Lowe C P 2005 Phys. Rev. Lett. 94 148104

    Article  Google Scholar 

  7. Römer F and Fedosov D A 2015 Europhys. Lett. 109 68001

    Article  Google Scholar 

  8. Shendruk T N, Hickey O A, Slater G W and Hardenv J L 2012 Curr. Opin. Colloid Interface Sci. 17 74

    Article  CAS  Google Scholar 

  9. Long D and Ajdari A 2001 Eur. Phys. J. E 4 29

    Article  CAS  Google Scholar 

  10. Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M et al 2013 Rev. Mod. Phys. 85 1143

    Article  CAS  Google Scholar 

  11. Savina M, Lacroix G and Ruddick K 2010 J. Marine Syst. 81 86

    Article  Google Scholar 

  12. Versteeg H K and Malalasekera W 1995 An introduction to computational fluid dynamics: the finite volume method (Pearson Education)

  13. Succi S 2001 The lattice Boltzmann equation: for fluid dynamics and beyond (Oxford: Oxford University Press)

    Google Scholar 

  14. Hao L and Cheng P 2009 J. Power Sources 190 435

    Article  CAS  Google Scholar 

  15. Gupta A and Kumar R 2008 ASME paper no. ICNMM2008-62372

  16. Ladd A J C 1994 J. Fluid Mech. 271 285

    Article  CAS  Google Scholar 

  17. Ladd A J C 1994 J. Fluid Mech. 271 311

    Article  CAS  Google Scholar 

  18. Denniston C, Orlandini E and Yeomans J M 2001 Phys. Rev. E 63 05670

    Article  Google Scholar 

  19. Singh S, Subramanian G and Ansumali S 2011 Phil. Trans. R. Soc. A 369 2301

    Article  Google Scholar 

  20. de Graaf J and Stenhammar J 2017 Phys. Rev. E 95 023302

    Article  Google Scholar 

  21. Drescher K, Dunkel J, Cisneros L H, Ganguly S and Goldstein R E 2011 Proc. Natl. Acad. Sci. 108 10940

    Article  CAS  Google Scholar 

  22. Kokot G, Kolmakov G V, Aranson S and Snezhko A 2017 Sci. Rep. 7 14726

    Article  Google Scholar 

  23. Chen C H, Abate R A, Lee D, Terentjev E M and Weitz D A 2009 Adv. Mater. 21 3201

    Article  CAS  Google Scholar 

  24. Rettinger C and Rüde U 2017 Comput. Fluids 154 74

    Article  Google Scholar 

  25. Feng Z G and Michaelides E E 2004 J. Comput. Phys. 195 602

    Article  Google Scholar 

  26. Faviera J, Revellb A and Pinelli A 2014 J. Comput. Phys. 261 145

    Article  Google Scholar 

  27. Kim S and Karrila S J 1991 Microhydrodynamics (Butterworth-Heinemann)

  28. Aidun C K and Clausen J R 2010 Annu. Rev. Fluid Mech. 42 43972

    Article  Google Scholar 

  29. Burden R L and Faires J D 2011 Numerical analysis (Brooks/Cole, Cengage Learning)

  30. Guazzelli E, Morris J F and Pic S 2011 A physical introduction to suspension dynamics (Cambridge University Press)

  31. Jeffrey D J and Onishi Y 1981 J. Mech. Appl. Math. 2 129

    Article  Google Scholar 

  32. Ishimoto K and Crowdy D G 2017 J. Fluid Mech. 821 647

    Article  Google Scholar 

  33. Liu B, Kenneth S B and Powers T R 2014 Phys. Fluids 26 011701

    Article  Google Scholar 

  34. Wu H, Thiebaud M, Hu W F, Farutin A, RafaıS, Lai M C et al 2015 Phys. Rev. E 92 050701(R)

    Article  Google Scholar 

  35. Lighthill M J 1952 Commun. Pure Appl. Maths 5 109

    Article  Google Scholar 

  36. Blake J R 1971 J. Fluid Mech. 46 199

    Article  Google Scholar 

  37. Blake J R 1971 Bull. Austral. Math. Soc. 5 255

    Article  Google Scholar 

  38. Pedley T J 2016 IMA J. Appl. Math. 488 521

    Google Scholar 

  39. Gamayunov N I, Mantrov G I and Murtsovkin V A 1992 Colloid J. 54 20

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology, Madras, 600036, India

    Ahana Purushothaman & Sumesh P Thampi

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  1. Ahana Purushothaman
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  2. Sumesh P Thampi
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Correspondence to Ahana Purushothaman.

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Purushothaman, A., Thampi, S.P. Colloidal hydrodynamics using a quasi-steady algorithm in lattice Boltzmann method. Bull Mater Sci 43, 177 (2020). https://doi.org/10.1007/s12034-020-2074-z

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  • DOI: https://doi.org/10.1007/s12034-020-2074-z

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