Skip to main content
SpringerLink
Log in

Numerical study on hydrodynamics of a soft particle and sustained solute release

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The impact of the porous shell on the hydrodynamics of a core-shell (soft) particle is studied for low to moderate values of Reynolds number. The Reynolds number is based on the migration speed and radius of the core-shell particle. The influence of shell-to-core thickness ratio and permeability of the shell at a fixed Reynolds number is analyzed. The flow within the porous shell is governed by the Darcy–Brinkman–Forchheimer extended model and the Navier–Stokes equations in the clear fluid region. A single-domain approach in which two sets of equations for the fluid and the porous regions are combined into one set by introducing a binary parameter is adopted. Our numerical results are in excellent agreement with the analytic solution based on the Stokes–Brinkman model for a lower range of the Reynolds number. The computed solution based on the present model deviates from the linear model for a Reynolds number beyond 0.1. We found that the nonlinearity effects become strong as the permeability of the shell decreases. The influence of the Reynolds number on hydrodynamics and flow separation from the core-shell particle is studied. Our result for low Reynolds number shows that the mechanism of sustained solute release from the shell is initially dominated by diffusion; however, the fluid inertia effect becomes strong at the later stage, and a plume of solute is observed even at a low Reynolds number (Re < 1).

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. Hsu J.P., Hsieh Y.H.: Boundary effect on the drag force on a nonhomogeneous floc. J. Colloid Interface Sci. 264, 517–525 (2003)

    Article  Google Scholar 

  2. Abade G.C., Cichocki B., Ekiel-Jezewska M.L., Ngele G., Wajnryb E.: Diffusion, sedimentation, and rheology of concentrated suspensions of core-shell particles. J. Chem. Phys. 136, 104902 (2012)

    Article  Google Scholar 

  3. Hill R.J., Li F.: Hydrodynamic drag coeffcient for soft core-shell nanoparticles in hydrogels. Chem. Eng. Sci. 89, 1–9 (2013)

    Article  Google Scholar 

  4. Pinho S.L.C., Laurent S., Rocha J., Roch A., Delville M., Mornet S., Carlos L.D., Elst L.V., Muller R.N., Geraldes C.F.G.C.: Relaxometric studies of γ−Fe 2 O 3@SiO 2 core shell nanoparticles: when the coating matters. J. Phys. Chem. C 116, 2285–2291 (2012)

    Article  Google Scholar 

  5. Neale G., Epstein N., Nader W.: Creeping flow relative to permeable spheres. Chem. Eng. Sci. 28, 1865–1874 (1973)

    Article  Google Scholar 

  6. Masliyah J.H., Neale G., Malysa K., Ven T.G.M.V.D.: Creeping flow over a composite sphere: Solid core with porous shell. Chem. Eng. Sci. 42, 245–253 (1987)

    Article  Google Scholar 

  7. Anderson J.L., McKenzie P.F., Webber R.M.: Model for hydrodynamic thickness of thin polymer layers at solid/liquid interfaces. Langmuir 7, 162–166 (1991)

    Article  Google Scholar 

  8. Veerapaneni S., Wiesner M.R.: Hydrodynamics of fractal aggregates with radially varying permeability. J. Colloid Interface Sci. 177, 45–57 (1996)

    Article  Google Scholar 

  9. Vanni M.: Creeping flow over spherical permeable aggregates. Chem. Eng. Sci. 55, 685–698 (2000)

    Article  Google Scholar 

  10. Li X.Y., Logan B.E.: Permeability of fractal aggregates. Water Res. 35, 3373–3380 (2001)

    Article  Google Scholar 

  11. Vainshtein P., Shapiro M., Gutfinger C.: Mobility of permeable aggregates: effects of shape and porosity. Aerosol Sci. 35, 383–404 (2004)

    Article  Google Scholar 

  12. Vainshtein P., Shapiro M.: Mobility of permeable fractal agglomerates in slip regime. J. Colloid Interface Sci. 284, 501–509 (2005)

    Article  Google Scholar 

  13. Zackrisson M., Bergenholtz J.: Intrinsic viscosity of dispersions of core-shell particles. Colloids Surf. A Physicochem. Eng. Aspects 225, 119–127 (2003)

    Article  Google Scholar 

  14. Cichocki B., Ekiel-Jezewska M.L., Wajnryb E.: Short-time dynamics and high-frequency rheology of suspensions of spherical core-shell particles with thin-shells. Colloids Surf. A Physicochem. Eng. Aspects 418, 22–28 (2013)

    Article  Google Scholar 

  15. Coutinho C.A., Harrinauth R.K., Gupta V.K.: Settling characteristics of composites of PNIPAM microgels and TiO 2 nanoparticles. Colloids Surf. A: Physicochem. Eng. Aspects 318, 111–121 (2008)

    Article  Google Scholar 

  16. Lee D.J., Chen G.W., Liao Y.C., Hsieh C.C.: On the free-settling test for estimating activated sludge floc density. Water Res. 30, 541–550 (1996)

    Article  Google Scholar 

  17. Hee P.V., Hoeben M.A., Lans R.G.J.M.V.D., Wielen L.A.M.V.D.: Strategy for selection of methods for separation of bioparticles from particle mixtures. Biotechnol. Bioeng. 94, 689–709 (2006)

    Article  Google Scholar 

  18. Mahmoud A., Olivier J., Vaxelaire J., Hoadley A.F.: Electrical field: a historical review of its application and contributions in wastewater sludge dewatering. Water Res. 44, 2381–2407 (2010)

    Article  Google Scholar 

  19. Xiao F., Li X., Lam K., Wang D.: Investigation of the hydrodynamic behavior of diatom aggregates using particle image velocimetry. J. Environ. Sci. 24, 1157–1164 (2012)

    Article  Google Scholar 

  20. Johnson T.A., Patel V.C.: Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19–70 (1999)

    Article  Google Scholar 

  21. Fourar M., Radilla G., Lenormand R., Moyne C.: On the non-linear behavior of a laminar single-phase flow through two and three-dimensional porous media. Adv. Water Res. 27, 669–677 (2004)

    Article  Google Scholar 

  22. Nield A.D., Bejan A.: Convection in Porous Media. Springer, New York (2005)

    Google Scholar 

  23. Ingham D.B., Pop I.: Transport phenomena in porous media. Elsevier, Oxford (2005)

    Google Scholar 

  24. Bhattacharyya S., Dhinakaran S., Khalili A.: Fluid motion around and through a porous cylinder. Chem. Eng. Sci. 61, 4451–4461 (2006)

    Article  Google Scholar 

  25. Li X.Y., Yuan Y., Wang H.W.: Hydrodynamics of biological aggregates of different sludge ages: an insight into the mass transport mechanisms of bioaggregates. Environ. Sci. Technol. 37, 292–299 (2003)

    Article  Google Scholar 

  26. Arifin D.Y., Lee L.Y., Wang C.H.: Mathematical modeling and simulation of drug release from microspheres: implications to drug delivery systems. Adv. Drug Deliv. Rev. 58, 1274–1325 (2006)

    Article  Google Scholar 

  27. Rastogi V., Velikovb K.P., Velev O.D.: Microfluidic characterization of sustained solute release from porous supraparticles. Phys. Chem. Chem. Phys. 12, 11975–11983 (2010)

    Article  Google Scholar 

  28. Li X.Y., Yuan Y.: Settling velocities and permeabilities of microbial aggregates. Water Res. 36, 3110–3120 (2002)

    Article  Google Scholar 

  29. Hsu C.T., Cheng P.: Thermal dispersion in a porous medium. Int. J. Heat Mass Transfer 33, 1587–1597 (1990)

    Article  MATH  Google Scholar 

  30. Fletcher C.A.J.: Computation Technique for Fluid Dynamics, vol. 2. Springer, Berlin (1998)

    Google Scholar 

  31. Leonard B.P.: A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Eng. 19, 59–98 (1979)

    Article  MATH  Google Scholar 

  32. Feng Z.G., Michaelides E.E.: Heat and mass transfer coefficients of viscous spheres. Int. J. Heat Mass Transfer 44, 4445–4454 (2001)

    Article  MATH  Google Scholar 

  33. Nandakumar K., Masliyah J.H.: Laminar flow past a permeable sphere. Can. J. Chem. Eng. 60, 202–211 (1982)

    Article  Google Scholar 

  34. Kuwabara S.: The forces experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds number. J. Phys. Soc. Jpn. 14, 527–532 (1959)

    Article  MathSciNet  Google Scholar 

  35. Breugem W.P., Boersma B.J., Uittenbogaard R.E.: The laminar boundary layer over a permeable wall. Transp. Porous Media 59, 267–300 (2005)

    Article  MathSciNet  Google Scholar 

  36. Ohshima H.: Sedimentation potential and velocity in a concentrated suspension of soft particles. J. Colloid Interface Sci. 229, 140–147 (2000)

    Article  Google Scholar 

  37. Keh H.j., Chen W.C.: Sedimentation velocity and potential in concentrated suspensions of charged porous spheres. J. Colloid Interface Sci. 296, 710–720 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    S. Bhattacharyya & Simanta De

Authors
  1. S. Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Simanta De
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Bhattacharyya.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhattacharyya, S., De, S. Numerical study on hydrodynamics of a soft particle and sustained solute release. Acta Mech 226, 611–624 (2015). https://doi.org/10.1007/s00707-014-1217-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-014-1217-y

Keywords

Search

Navigation