Skip to main content
SpringerLink
Log in

Effect of viscosity ratio on the motion of drops flowing on an inclined surface

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

The flow of two-dimensional drops on an inclined channel is studied by numerical simulations at finite Reynolds numbers. The effect of viscosity ratio on the behaviour of the two-phase medium is examined. The flow is driven by the acceleration due to gravity, and there is no pressure gradient along the flow direction. An implicit version of the finite difference/front-tracking method was developed and used in the present study. The lateral migration of a drop is studied first. It is found that the equilibrium position of a drop moves away from the channel floor as the viscosity ratio increases. However, the trend reverses beyond a certain viscosity ratio. Simulations with 40 drops in a relatively large channel show that there exists a limiting viscosity ratio where the drops behave like solid particles, and the effect of internal circulation of drops becomes negligible. This limiting condition resembles the granular flow regime except that the effect of interstitial fluid is present. The limiting viscosity ratio depends on the flow conditions (80 for \(Re=10\), and 200 for \(Re=20\)). There are two peaks in the areal fraction distribution of drops across the channel which is different from granular flow regime. It is also found that the peak in areal fraction distribution of drops moves away from the channel floor as the inclination angle of the channel increases.

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. Adams, J.: Multigrid Fortran software for the efficient solution of linear elliptic partial differential equations. Appl. Math. Comput. 34, 113–146 (1989)

    MATH  Google Scholar 

  2. Bayareh, M., Mortazavi, S.: Three-dimensional numerical simulation of drops suspended in simple shear flow at finite Reynolds numbers. Int. J. Multiph. Flow 37, 1315–1330 (2011)

    Article  MATH  Google Scholar 

  3. Campbell, C.S., Brennen, C.E.: Chute flows of granular material: some computer simulations. J. Appl. Mech. 52, 172–178 (1985)

    Article  Google Scholar 

  4. Coulliette, C., Pozrikidis, C.: Motion of an array of drops through a cylindrical tube. J. Fluid Mech. 358, 1–28 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Feng, J., Hu, H.H., Joseph, D.D.: Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 261, 271–301 (1994)

    Article  MATH  Google Scholar 

  6. Goldsmith, H.L., Mason, S.G.: The flow of suspensions through tubes. I. Single spheres, rods, and discs. J. Colloid Sci. 17, 448–476 (1962)

    Article  Google Scholar 

  7. Griggs, A.J., Zinchenko, A.Z., Davis, R.H.: Gravity-driven motion of a drop or bubble near an inclined plane at low Reynolds number. Int. J. Multiph. Flow 34, 408–413 (2008)

    Article  Google Scholar 

  8. Harlow, F.H., Eddie Welch, J.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182–2189 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ho, B.P., Leal, L.G.: Inertial migration of rigid spheres in two-dimensional unidirectional flows. J. Fluid Mech. 65, 365–400 (1974)

    Article  MATH  Google Scholar 

  10. Janssen, P.J.A., Anderson, P.D.: A boundary-integral model for drop deformation between two parallel plates with non-unit viscosity ratio drops. J. Comput. Phys. 227, 8807–8819 (2008)

    Article  MATH  Google Scholar 

  11. Karnis, A., Goldsmith, H.L., Mason, S.G.: Axial migration of particles in Poiseuille flow. Nature 200, 159–160 (1963)

    Article  Google Scholar 

  12. Karnis, A., Goldsmith, H.L., Mason, S.G.: The flow of suspensions through tubes: V. Inertial effects. Can. J. Chem. Eng. 44, 181–193 (1966)

    Article  Google Scholar 

  13. Kowalewski, T.A.: Concentration and velocity measurements in the flow of droplet suspensions through tube. Exp. Fluids 2, 213–219 (1984)

    Article  Google Scholar 

  14. Li, X., Pozrikidis, C.: Film flow of a suspension of liquid drops. Phys. Fluids 14, 61–74 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mortazavi, S., Tryggvason, G.: A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop. J. Fluid Mech. 41, 325–350 (2000)

    Article  MATH  Google Scholar 

  16. Mortazavi, S., Tafreshi, M.M.: On the behavior of suspension of drops on an inclined surface. Phys. A 392, 58–71 (2013)

    Article  Google Scholar 

  17. Nourbakhsh, A., Mortazavi, S., Afshar, Y.: Three-dimensional numerical simulation of drops suspended in Poiseuille flow at non-zero Reynolds numbers. Phys. Fluids 23, 123303–123311 (2011)

    Article  Google Scholar 

  18. Oliver, D.R., Silberberg, A.: Influence of particle rotation on radial migration in the Poiseuille flow of suspensions. Nature 194, 1269–1271 (1962)

    Article  Google Scholar 

  19. Peyret, R., Taylor, T.D.: Computational Methods for Fluid Flow. Springer, Berlin (1983)

    Book  MATH  Google Scholar 

  20. Segre, G., Silberberg, A.: Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209–210 (1961)

    Article  Google Scholar 

  21. Segre, G., Silberberg, A.: Behavior of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams. J. Fluid Mech. 14, 115–135 (1962)

    Article  MATH  Google Scholar 

  22. Segre, G., Silberberg, A.: Behavior of macroscopic rigid spheres in Poiseuille flow Part II. Experimental results and interpretation. J. Fluid Mech. 14, 136–157 (1962)

    Article  MATH  Google Scholar 

  23. Unverdi, S.O., Tryggvason, G.: A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37 (1992)

    Article  MATH  Google Scholar 

  24. Zhou, H., Pozrikidis, C.: Pressure-driven flow of suspensions of liquid drops. Phys. Fluids 6, 80–94 (1994)

    Article  Google Scholar 

  25. Zhou, H., Pozrikidis, C.: The flow of ordered and random suspensions of two-dimensional drops in a channel. J. Fluid Mech. 255, 103–127 (1993)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    M. Aberuee & S. Mortazavi

Authors
  1. M. Aberuee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mortazavi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Mortazavi.

Additional information

Communicated by Tim Phillips.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aberuee, M., Mortazavi, S. Effect of viscosity ratio on the motion of drops flowing on an inclined surface. Theor. Comput. Fluid Dyn. 32, 73–90 (2018). https://doi.org/10.1007/s00162-017-0438-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-017-0438-9

Keywords

Search

Navigation