Skip to main content
SpringerLink
Log in

Slip Flow of a Shear-Thinning Power-Law Fluid Past an Assemblage of Spherical Particles

  • Conference paper
  • First Online:
Fluid Mechanics and Fluid Power – Contemporary Research

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

  • 4842 Accesses

Abstract

The momentum transfer characteristics of slip flow around an assemblage of spherical particles in a shear-thinning fluid (n = 0.6) is numerically studied. At fluid-solid interface a linear slip velocity is applied. As the non-dimensional slip number (λ) increases, the fluid slip becomes weaker i.e., λ = 0 represents fully slip flow and λ = ∞ indicate no-slip velocity at the solid-fluid interface. A finite difference method based on SMAC semi-implicit algorithm is used in this work over the range of conditions as: Reynolds number, Re = 100–200, power-law behavior index, n = 0.6, volume fraction of slip spheres, Φ = 0.1, and dimensionless slip parameter, λ = 0.01–100. Finally effects of these parameters on detailed flow kinematics are discussed in details.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

C d :

Total drag coefficient

C df :

Friction drag coefficient

C dp :

Pressure drag coefficient

F d :

Drag force (N)

p :

Pressure

r :

Radial distance

R :

Sphere radius (m)

λ :

Slip number

Re :

Reynolds number

R ∞ :

Cell boundary

U :

Free stream velocity (m/s)

v r :

r-component of velocity

v θ :

θ-component of velocity

Φ :

Volume fraction of slip spheres

ε:

Rate of strain tensor

η:

Fluid viscosity

ρ:

Fluid density (kg/m3)

τ:

Extra stress tensor

References

  1. Hatzikiriakos, S.G.: Wall slip of molten polymers. Prog. Polym. Sci. 37, 624–643 (2012)

    Article  Google Scholar 

  2. Moshfegh, M., Shams, G., Ebrahim, A.R.: A novel slip correction factor for spherical aerosol particles. Eng. Technol. 46, 108–114 (2008)

    Google Scholar 

  3. Elasmi, L., Feuillebois, F.: Green function for a Stokes flow near a porous slab. ZAMP 81, 743–752 (2001)

    MathSciNet  MATH  Google Scholar 

  4. Chillcott, M.D., Rallison, J.M.: Creeping flow of dilute polymer solutions past cylinders and spheres. J. Nonnewton. Fluid Mech. 29, 381–432 (1988)

    Article  MATH  Google Scholar 

  5. Sochi, T.: Slip at fluid-solid interface. Polym. Rev. 51, 309–340 (2011)

    Article  Google Scholar 

  6. Palani, N., Ramalingam, V., Ramadoss, G., Seeniraj, R.V.: Study of slip velocity and application of drift-flux model to slip velocity in a liquid-solid circulating fluidized bed. Adv. Powder Technol. 22, 77–85 (2011)

    Article  Google Scholar 

  7. Hatzikiriakos, S.G., Dealy, J.M.: Wall slip of molten high density polyethylene: II. Capillary rheometer studies. J. Rheol. 36, 703–741 (1992)

    Article  Google Scholar 

  8. Hatzikiriakos, S.G., Dealy, J.M.: Wall slip of molten high density polyethylene: I. Sliding plate rheometer studies. J. Rheol. 35, 497–523 (1991)

    Article  Google Scholar 

  9. Luk, S., Mutharasan, R., Apelian, D.: Experimental observation of wall slip: tube and packed bed flow. Ind. Eng. Chem. Res. 26, 1609–1616 (1987)

    Article  Google Scholar 

  10. Denn, M.M.: Extrusion instabilities and wall slip. Ann. Rev. Fluid Mech. 22, 265–287 (2001)

    Article  MATH  Google Scholar 

  11. Neto, C., Evans, D.R., Bonaccurso, E., Butt, H.J., Craig, V.S.J.: Boundary slip in Newtonian liquid: a review of experimental studies. Rep. Prog. Phys. 68, 2859–2897 (2005)

    Article  Google Scholar 

  12. Keh, H.J., Chen, S.H.: The motion of a slip spherical particle in an arbitrary Stokes flow. Eur. J. Mech. B/Fluids 15, 791–807 (1996)

    MATH  Google Scholar 

  13. Datta, S., Singhal, S.: Slip flow past a sphere with a source at its centre. Int. J. Appl. Math Mech. 7, 36–51 (2011)

    MATH  Google Scholar 

  14. Kumar, A., Hodgson, P., Fabijanic, D., Gao, W.: Numerical solution of gas-solid flow in fluidized bed at sub-atmospheric pressures. Adv. Powder Technol. 23, 485–492 (2012)

    Article  Google Scholar 

  15. Luo, H., Pozrikidis, C.: Effect of surface slip on Stokes flow past a spherical particle in infinite fluid and near a plane wall. J. Eng. Math. 62, 1–21 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Reed, L.D., Morrison, F.A.: Particle interactions in viscous flow at small values of Knudesen number. J. Aerosol Sci. 5, 175–189 (1974)

    Article  Google Scholar 

  17. Padmavathi, B.S., Amaranath, T., Nigam, S.D.: Stokes flow past a sphere with mixed slip-stick boundary conditions. Fluid Dyn. Res. 11, 229–234 (1993)

    Article  MATH  Google Scholar 

  18. Faltas, M.S., Saad, E.I.: Stokes flow past an assemblage of slip eccentric spherical particle-in-cell models. Math. Methods Appl. Sci. 34, 1594–1605 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Happel, J.: Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. AIChE J. 4, 197–201 (1958)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Bird, B.R., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. John-Wiley, New York (1987)

    Google Scholar 

  22. Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surfaces. Phys. Fluids 8, 2182–2188 (1965)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  24. Gummalam, S., Chhabra, R.P.: Rising velocity of swarm of bubbles in a power-law non-Newtonian liquid. Can. J. Chem. Eng. 65, 1004–1008 (1987)

    Article  Google Scholar 

  25. Jaiswal, A.K., Sundararajan, T., Chhabra, R.P.: Flow of power law liquids through particle assemblages at intermediate Reynolds numbers. Can. J. Chem. Eng. 69, 1235–1241 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Indian Institute of Technology Guwahati, Guwahati, 781039, Assam, India

    Rahul R. Ramteke &  Nanda Kishore

Authors
  1. Rahul R. Ramteke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nanda Kishore
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nanda Kishore .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Arun K. Saha

  2. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Debopam Das

  3. Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Rajesh Srivastava

  4. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    P. K. Panigrahi

  5. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    K. Muralidhar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer India

About this paper

Cite this paper

Ramteke, R.R., Nanda Kishore (2017). Slip Flow of a Shear-Thinning Power-Law Fluid Past an Assemblage of Spherical Particles. In: Saha, A., Das, D., Srivastava, R., Panigrahi, P., Muralidhar, K. (eds) Fluid Mechanics and Fluid Power – Contemporary Research. Lecture Notes in Mechanical Engineering. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2743-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-81-322-2743-4_2

  • Published:

  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2741-0

  • Online ISBN: 978-81-322-2743-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation