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Effect of Ionic Strength on the Electro-Dipping Force

  • Galina Lyutskanova–ZhekovaEmail author
  • Krassimir Danov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)

Abstract

The calculation of electro-dipping force, acting on a dielectric particle, attached to the boundary between water and nonpolar fluid, is important for the characterization of the surface charge density of micron-size objects and their three-phase contact angles [1]. The problem was solved semi-analytically, using the Mahler–Fox transformation in the simplified case of one phase with infinite dielectric permittivity [4]. We generalize this approach, taking into consideration the finite dielectric permittivity of the polar phase. We propose a numerical method for calculating the distribution of the electrostatic potential in all phases and the respective values of the dimensionless electro-dipping force. The expression for the weak singularity parameter at the three-phase contact line is analytically derived. In all studied cases, it is weaker than that in the model case [2]. The obtained results show that: (i) the electrostatic potential distribution is close to that in the model case for micron-size particles, large values of the ionic strength and dielectric constant of the polar phase; (ii) the force, arising from the electrostatic field in the polar phase, cannot be neglected for small (nano-size) particles and low ionic strengths.

Keywords

Electrostatic potential distribution Laplace equations Complex numerical domains and boundary conditions Toroidal coordinates 

References

  1. 1.
    Lotito, V., Zambelli, T.: Approaches to self-assembly of colloidal monolayers: a guide to nanotechnologists. Adv. Colloid Interface Sci. 246, 217–274 (2017)CrossRefGoogle Scholar
  2. 2.
    Danov, K., Kralchevsky, P., Boneva, M.: Electrodipping force acting on solid particles at a fluid interface. Langmuir 20(15), 6139–6151 (2004)CrossRefGoogle Scholar
  3. 3.
    Horozov, T., Aveyard, R., Binks, P., Clint, J.: Structure and stability of silica particle monolayers at horizontal and vertical octane-water interfaces. Langmuir 21(16), 7405–7412 (2005)CrossRefGoogle Scholar
  4. 4.
    Danov, K., Kralchevsky, P.: Electric forces induced by a charged colloid particle attached to the water-nonpolar fluid interface. J. Colloid Interface Sci. 298(1), 213–231 (2006)CrossRefGoogle Scholar
  5. 5.
    Danov, K., Kralchevsky, P.: Forces acting on dielectric colloidal spheres at a water/nonpolar fluid interface in an external electric field. 2. charged particles. J. Colloid Interface Sci. 405, 269–277 (2013)CrossRefGoogle Scholar
  6. 6.
    Wang, Y., Wang, T.: A compact ADI method and its extrapolation for time fractional sub-diffusion equations with nonhomogeneous Neumann boundary conditions. Comput. Math. Appl. 75(3), 721–739 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Galina Lyutskanova–Zhekova
    • 1
    • 2
    Email author
  • Krassimir Danov
    • 3
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria
  3. 3.Faculty of Chemistry and PharmacySofia UniversitySofiaBulgaria

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