Application of Tunable-Slip Boundary Conditions in Particle-Based Simulations

  • Jiajia Zhou
  • Jens Smiatek
  • Evgeny S. Asmolov
  • Olga I. Vinogradova
  • Friederike Schmid
Conference paper


Compared to macroscopic systems, fluids on the micro- and nanoscales have a larger surface-to-volume ratio, thus the boundary condition becomes crucial in determining the fluid properties. No-slip boundary condition has been applied successfully to wide ranges of macroscopic phenomena, but its validity in microscopic scale is questionable. A more realistic description is that the flow exhibits slippage at the surface, which can be characterized by a Navier slip length. We present a tunable-slip method by implementing Navier boundary condition in particle-based computer simulations (Dissipative Particle Dynamics as an example). To demonstrate the validity and versatility of our method, we have investigated two model systems: (i) the flow past a patterned surface with alternating no-slip/partial-slip stripes and (ii) the diffusion of a spherical colloidal particle.


  1. 1.
    Squires, T.M., Quake, S.R.: Microfluidics: Fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977 (2005)CrossRefGoogle Scholar
  2. 2.
    Bocquet, L., Barrat, J.L.: Flow boundary conditions from nano- to micro-scales. Soft Matter 3, 685 (2007)CrossRefGoogle Scholar
  3. 3.
    Hoogerbrugge, P.J., Koelman, J.M.V.A.: Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19, 155 (1992)CrossRefGoogle Scholar
  4. 4.
    Español, P., Warren, P.B.: Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30, 191 (1995)CrossRefGoogle Scholar
  5. 5.
    Groot, R.D., Warren, P.B.: Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 107, 4423 (1997)CrossRefGoogle Scholar
  6. 6.
    Smiatek, J., Allen, M., Schmid, F.: Tunable-slip boundaries for coarse-grained simulations of fluid flow. Eur. Phys. J. E 26, 115 (2008)CrossRefGoogle Scholar
  7. 7.
    Weeks, J.D., Chandler, D., Andersen, H.C.: Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237 (1971)CrossRefGoogle Scholar
  8. 8.
    Vinogradova, O.I.: Drainage of a thin liquid film confined between hydrophobic surfaces. Langmuir 11, 2213 (1995)CrossRefGoogle Scholar
  9. 9.
    Philip, J.R.: Flows satisfying mixed no-slip and no-shear conditions. J. Appl. Math. Phys. 23, 353 (1972)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Lauga, E., Stone, H.A.: Effective slip in pressure-driven stokes flow. J. Fluid Mech. 489, 55 (2003)Google Scholar
  11. 11.
    Belyaev, A.V., Vinogradova, O.I.: Effective slip in pressure-driven flow past superhydrophobic stripes. J. Fluid Mech. 652, 489 (2010)Google Scholar
  12. 12.
    Zhou, J., Belyaev, A.V., Schmid, F., Vinogradova, O.I.: Anisotropic flow in striped superhydrophobic channels. J. Chem. Phys. 136, 194706 (2012)CrossRefGoogle Scholar
  13. 13.
    Asmolov, E.S., Zhou, J., Schmid, F., Vinogradova, O.I.: Effective slip-length tensor for a flow over weakly slipping stripes. Phys. Rev. E 88, 023004 (2013)CrossRefGoogle Scholar
  14. 14.
    Zhou, J., Asmolov, E.S., Schmid, F., Vinogradova, O.I.: Effective slippage on superhydrophobic trapezoidal grooves. J. Chem. Phys. 139, 174708 (2013)CrossRefGoogle Scholar
  15. 15.
    Smiatek, J., Sega, M., Holm, C., Schiller, U.D., Schmid, F.: Mesoscopic simulations of the counterion-induced electro-osmotic flow: A comparative study. J. Chem. Phys. 130, 244702 (2009)CrossRefGoogle Scholar
  16. 16.
    Smiatek, J., Schmid, F.: Polyelectrolyte electrophoresis in nanochannels: A dissipative particle dynamics simulation. J. Phys. Chem. B 114, 6266 (2010)CrossRefGoogle Scholar
  17. 17.
    Smiatek, J., Schmid, F.: Mesoscopic simulations of polyelectrolyte electrophoresis in nanochannels. Comput. Phys. Commun. 182, 1941 (2011)CrossRefGoogle Scholar
  18. 18.
    Meinhardt, S., Smiatek, J., Eichhorn, R., Schmid, F.: Separation of chiral particles in micro- or nanofluidic channels. Phys. Rev. Lett. 108, 214504 (2012)CrossRefGoogle Scholar
  19. 19.
    Russel, W.B., Saville, D.A., Schowalter, W.: Colloidal Dispersions. Cambridge University Press, Cambridge (1989)CrossRefGoogle Scholar
  20. 20.
    Dhont, J.: An Introduction to Dynamics of Colloids. Elsevier, Amsterdam (1996)Google Scholar
  21. 21.
    Ahlrichs, P., Dünweg, B.: Simulation of a single polymer chain in solution by combining lattice boltzmann and molecular dynamics. J. Chem. Phys. 111, 8225 (1999)CrossRefGoogle Scholar
  22. 22.
    Lobaskin, V., Dünweg, B.: A new model for simulating colloidal dynamics. New J. Phys. 6, 54 (2004)CrossRefGoogle Scholar
  23. 23.
    Chatterji, A., Horbach, J.: Combining molecular dynamics with lattice boltzmann: A hybrid method for the simulation of (charged) colloidal systems. J. Chem. Phys. 122, 184903 (2005)CrossRefGoogle Scholar
  24. 24.
    Hasimoto, H.: On the periodic fundamental solutions of the stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317 (1959)CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Zhou, J., Schmid, F.: Dielectric response of nanoscopic spherical colloids in alternating electric fields: a dissipative particle dynamics simulation. J. Phys. Condens. Matter 24, 464112 (2012)CrossRefGoogle Scholar
  26. 26.
    Zhou, J., Schmid, F.: AC-field-induced polarization for uncharged colloids in salt solution: a dissipative particle dynamics simulation. Eur. Phys. J. E 36, 33 (2013)CrossRefGoogle Scholar
  27. 27.
    Zhou, J., Schmitz, R., Dünweg, B., Schmid, F.: Dynamic and dielectric response of charged colloids in electrolyte solutions to external electric fields. J. Chem. Phys. 139, 024901 (2013)CrossRefGoogle Scholar
  28. 28.
    Zhou, J., Schmid, F.: Eur. Phys. Computer simulations of charged colloids in alternating electric fields. J. Spec. Top. 222, 2911 (2013)Google Scholar
  29. 29.
    Swan, J.W., Khair, A.S.: On the hydrodynamics of ‘slip-slick’ spheres. J. Fluid Mech. 606, 115 (2008)CrossRefMATHMathSciNetGoogle Scholar
  30. 30.
    Khair, A.S., Squires, T.M.: The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle. Phys. Fluids 21, 042001 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jiajia Zhou
    • 1
  • Jens Smiatek
    • 2
  • Evgeny S. Asmolov
    • 3
    • 4
    • 5
  • Olga I. Vinogradova
    • 3
    • 6
    • 7
  • Friederike Schmid
    • 1
  1. 1.Institut für PhysikJohannes Gutenberg-Universität MainzMainzGermany
  2. 2.Institut für ComputerphysikUniversität StuttgartStuttgartGermany
  3. 3.A.N. Frumkin Institute of Physical Chemistry and ElectrochemistryRussian Academy of ScienceMoscowRussia
  4. 4.Central Aero-Hydrodynamic InstituteZhukovsky, Moscow regionRussia
  5. 5.Institute of MechanicsM.V. Lomonosov Moscow State UniversityMoscowRussia
  6. 6.Department of PhysicsM.V. Lomonosov Moscow State UniversityMoscowRussia
  7. 7.DWI – Leibniz Institute for Interactive Materials, RWTH AachenAachenGermany

Personalised recommendations