Skip to main content
SpringerLink
Log in

Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility

  • Regular Article
  • Published:
The European Physical Journal E Aims and scope Submit manuscript

Abstract.

Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility.

Graphical abstract

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. Kimiko Makino, Hiroyuki Ohshima, Sci. Technol. Adv. Mater. 12, 023001 (2011)

    Google Scholar 

  2. Thanh H. Nguyen, Nickolas Easter, Leonardo Gutierrez, Lauren Huyett, Emily Defnet, Steven E. Mylon, James K. Ferri, Nguyen Ai Viet, Soft Matter 7, 10449 (2011)

    ADS  Google Scholar 

  3. Antonio Siber, Anže Lošdorfer Božič, Rudolf Podgornik, Phys. Chem. Chem. Phys. 14, 3746 (2012)

    Google Scholar 

  4. Antonio Siber, Rudolf Podgornik, Phys. Rev. E 76, 061906 (2007)

    ADS  Google Scholar 

  5. Hiroyuki Ohshima, J. Colloid Interface Sci. 252, 119 (2002)

    Google Scholar 

  6. Hiroyuki Ohshima, Electrophoresis 27, 526 (2006)

    Google Scholar 

  7. Hiroyuki Ohshima, Colloids Surf. A: Physicochem. Eng. Asp. 376, 72 (2011)

    Google Scholar 

  8. Hiroyuki Ohshima, Colloids Surf. A: Physicochem. Eng. Asp. 440, 151 (2014)

    Google Scholar 

  9. Jérôme F.L. Duval, Fabien Gaboriaud, Curr. Opin. Colloid Interface Sci. 15, 184 (2010)

    Google Scholar 

  10. Jérôme F.L. Duval, Vera I. Slaveykova, Monika Hosse, Jacques Buffle, Kevin J. Wilkinson, Biomacromolecules 7, 2818 (2006)

    Google Scholar 

  11. Jérôme F.L. Duval, Hiroyuki Ohshima, Langmuir 22, 3533 (2006)

    Google Scholar 

  12. Ralf Zimmermann, Gesine Gunkel-Grabole, Johanna Bünsow, Carsten Werner, Wilhelm T.S. Huck, Jérôme F.L. Duval, J. Phys. Chem. C 121, 2915 (2017)

    Google Scholar 

  13. Mariam Moussa, Celine Caillet, Raewyn M. Town, Jérôme F.L. Duval, Langmuir 31, 5656 (2015)

    Google Scholar 

  14. Ralf Zimmermann, Dirk Kuckling, Martin Kaufmann, Carsten Werner, Jérôme F.L. Duval, Langmuir 26, 18169 (2010)

    Google Scholar 

  15. Jenny Merlin, Jérôme F.L. Duval, Phys. Chem. Chem. Phys. 16, 15173 (2014)

    Google Scholar 

  16. D.A. Saville, J. Colloid Interface Sci. 222, 137 (2000)

    ADS  Google Scholar 

  17. Reghan J. Hill, D.A. Saville, W.B. Russel, J. Colloid Interface Sci. 263, 478 (2003)

    ADS  Google Scholar 

  18. Reghan J. Hill, D.A. Saville, Colloids Surf. A: Physicochem. Eng. Asp. 267, 31 (2005)

    Google Scholar 

  19. S. Bhattacharyya, Simanta De, Phys. Fluids 28, 012001 (2016)

    ADS  Google Scholar 

  20. Jyh-Ping Hsu, Zheng-Syun Chen, Langmuir 23, 6198 (2007)

    Google Scholar 

  21. Li-Hsien Yeh, Kuo-Ying Fang, Jyh-Ping Hsu, Shiojenn Tseng, Colloids Surf. B: Biointerfaces 88, 559 (2011)

    Google Scholar 

  22. Hsuan-Pei Hsu, Eric Lee, Electrochem. Commun. 15, 59 (2012)

    Google Scholar 

  23. Li-Hsien Yeh, Jyh-Ping Hsu, Shizhi Qian, Shiojenn Tseng, Electrochem. Commun. 19, 97 (2012)

    Google Scholar 

  24. Indrajit Roy, Tymish Y. Ohulchanskyy, Haridas E. Pudavar, Earl J. Bergey, Allan R. Oseroff, Janet Morgan, Thomas J. Dougherty, Paras N. Prasad, J. Am. Chem. Soc. 125, 7860 (2003)

    Google Scholar 

  25. Yongqiang Ren, Derek Stein, Nanotechnology 19, 195707 (2008)

    ADS  Google Scholar 

  26. Derek C. Tretheway, Carl D. Meinhart, Phys. Fluids 14, L9 (2002)

    ADS  Google Scholar 

  27. Olga I. Vinogradova, Int. J. Min. Process. 56, 31 (1999)

    Google Scholar 

  28. Yuki Uematsu, Roland R. Netz, Douwe Jan Bonthuis, Langmuir 34, 9097 (2018)

    Google Scholar 

  29. Majid Rezaei, Ahmad Reza Azimian, Ahmad Reza Pishevar, Douwe Jan Bonthuis, Phys. Chem. Chem. Phys. 20, 22517 (2018)

    Google Scholar 

  30. Yuki Uematsu, Roland R. Netz, Douwe Jan Bonthuis, Chem. Phys. Lett. 670, 11 (2017)

    ADS  Google Scholar 

  31. Douwe Jan Bonthuis, Roland R. Netz, J. Phys. Chem. B 117, 11397 (2013)

    Google Scholar 

  32. Christian Sendner, Dominik Horinek, Lyderic Bocquet, Roland R. Netz, Langmuir 25, 10768 (2009)

    Google Scholar 

  33. Thomas Lee, Eric Charrault, Chiara Neto, Adv. Colloid Interface Sci. 210, 21 (2014)

    Google Scholar 

  34. Aditya S. Khair, Todd M. Squires, Phys. Fluids 21, 042001 (2009)

    ADS  Google Scholar 

  35. Richard W. O’Brien, Lee R. White, J. Chem. Soc., Faraday Trans. 2: Mol. Chem. Phys. 74, 1607 (1978)

    Google Scholar 

  36. Partha P. Gopmandal, S. Bhattacharyya, H. Ohshima, Proc. R. Soc. A: Math. Phys. Eng. Sci. 473, 20160942 (2017)

    ADS  Google Scholar 

  37. Max Born, Z. Phys. A: Hadrons Nucl. 1, 45 (1920)

    Google Scholar 

  38. José Juan López-García, José Horno, Constantino Grosse, J. Colloid Interface Sci. 268, 371 (2003)

    ADS  Google Scholar 

  39. H.G.L. Coster, Biophys. J. 13, 133 (1973)

    ADS  Google Scholar 

  40. Ardalan Ganjizade, Seyed Nezameddin Ashrafizadeh, Arman Sadeghi, Electrochem. Commun. 84, 19 (2017)

    Google Scholar 

  41. Ardalan Ganjizade, Arman Sadeghi, Seyed Nezameddin Ashrafizadeh, Colloids Surf. B: Biointerfaces 170, 129 (2018)

    Google Scholar 

  42. Saurabh K. Maurya, Partha P. Gopmandal, S. Bhattacharyya, H. Ohshima, Phys. Rev. E 98, 023103 (2018)

    ADS  Google Scholar 

  43. Ardalan Ganjizade, Seyed Nezameddin Ashrafizadeh, Arman Sadeghi, Colloid Polym. Sci. 297, 191 (2019)

    Google Scholar 

  44. Jacob N. Israelachvili, Intermolecular and Surface Forces (Academic Press, 2015)

  45. J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265, 327 (2003)

    ADS  Google Scholar 

  46. C.A.J. Fletcher, Computational Techniques for Fluid Dynamics, Vol. 1 (Springer-Verlag, 1988) p. 302

  47. H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method (Addison-Wesley-Longman, 1995)

  48. Julián López-Viota, Subhra Mandal, Angel V. Delgado, José Luis Toca-Herrera, Marco Möller, Francesco Zanuttin, Maurizio Balestrino, Silke Krol, J. Colloid Interface Sci. 332, 215 (2009)

    ADS  Google Scholar 

  49. Partha P. Gopmandal, S. Bhattacharyya, H. Ohshima, Colloid Polym. Sci. 295, 2077 (2017)

    Google Scholar 

  50. Hung Mok Park, Electrophoresis 34, 651 (2013)

    Google Scholar 

  51. S.S. Dukhin, Adv. Colloid Interface Sci. 44, 1 (1993)

    Google Scholar 

  52. Stanislav Samuilovich Dukhin, Egon Matijevic, B.V. Derjaguin, Surface and Colloid Science, Vol. 7: Electrokinetic Phenomena (Wiley-Insterscience, 1974)

  53. Á.V. Delgado, F. González-Caballero, R.J. Hunter, L.K. Koopal, J. Lyklema, J. Colloid Interface Sci. 309, 194 (2007)

    ADS  Google Scholar 

  54. Naga Neehar Dingari, Cullen R. Buie, Langmuir 30, 4375 (2014)

    Google Scholar 

  55. Fei Li, Reghan J. Hill, J. Colloid Interface Sci. 394, 1 (2013)

    ADS  Google Scholar 

  56. Fei Li, Stuart A. Allison, Reghan J. Hill, J. Colloid Interface Sci. 423, 129 (2014)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Dipankar Kundu & Somnath Bhattacharyya

Authors
  1. Dipankar Kundu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Somnath Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Somnath Bhattacharyya.

Additional information

Publisher’s Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kundu, D., Bhattacharyya, S. Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility. Eur. Phys. J. E 43, 27 (2020). https://doi.org/10.1140/epje/i2020-11957-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/i2020-11957-8

Keywords

Search

Navigation