Skip to main content
SpringerLink
Log in

Study of the motion of a spheroidal drop in a linear shear flow

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The motion of a spheroidal deformable drop in a simple shear flow is simulated using a finite-difference/front-tracking method. The effect of surface tension coefficient, viscosity ratio and inertia on lateral migration and deformation of the drop is investigated. It is revealed that the deformation of a spheroidal drop is directly related to the capillary and Reynolds numbers. In the limit of finite Reynolds numbers, the equilibrium position of prolate drops depends strongly on the viscosity ratio; the final position of more viscous drops is closer to the wall in contrast with the spherical ones. As the deformability of drops increases and the inertial force decreases, the rate of migration of the prolate drops increases. Although the steady-state position does not depend on the capillary and Reynolds numbers, the migration rate depends considerably on these dimensionless parameters. In addition, the rate of migration is a decreasing function of the aspect ratio due to different direction of the lift force acting on the drop.

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.

Similar content being viewed by others

References

  1. G. Taylor, The formation of emulsions in definable fields of flow, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 146 (858) (1934) 501–523.

    Google Scholar 

  2. G. Segre and A. Silberberg, Behaviour of macroscopic rigid spheres in Poiseuille flow Part 1. Determination of local concentration by statistical analysis of particle passages through crossed light beams, Journal of Fluid Mechanics, 14 (1) (1962) 115–135.

    Article  MATH  Google Scholar 

  3. A. Esmaeeli and G. Tryggvason, Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays, Journal of Fluid Mechanics, 377 (1998) 313–345.

    Article  MATH  Google Scholar 

  4. S. Mortazavi and G. Tryggvason, A numerical study of the motion of drops in Poiseuille flow. Part 1. Lateral migration of one drop, Journal of Fluid Mechanics, 411 (2000) 325–350.

    Article  MATH  Google Scholar 

  5. A. Rust and M. Manga, Bubble shapes and orientations in low Re simple shear flow, Journal of Colloid and Interface Science, 249 (2) (2002) 476–480.

    Article  Google Scholar 

  6. B. Bunner and G. Tryggvason, Effect of bubble deformation on the properties of bubbly flows, Journal of Fluid Mechanics, 495 (2003) 77–118.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Lee and C. Pozrikidis, Effect of surfactants on the deformation of drops and bubbles in Navier–Stokes flow, Computers & Fluids, 35 (1) (2006) 43–60.

    Article  MATH  Google Scholar 

  8. E. Lac and D. Barthès-Biesel, Deformation of a capsule in simple shear flow: Effect of membrane prestress, Physics of Fluids, 17 (7) (2005) 072105.

    Article  MATH  Google Scholar 

  9. I. B. Bazhlekov, P. D. Anderson and H. E. Meijer, Numerical investigation of the effect of insoluble surfactants on drop deformation and breakup in simple shear flow, Journal of Colloid and Interface Science, 298 (1) (2006) 369–394.

    Article  Google Scholar 

  10. P. Bagchi, Mesoscale simulation of blood flow in small vessels, Biophysical Journal, 92 (6) (2007) 1858–1877.

    Article  Google Scholar 

  11. K. Feigl et al., Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants, Chemical Engineering Science, 62 (12) (2007) 3242–3258.

    Article  Google Scholar 

  12. M. Bayareh and S. Mortazavi, Numerical simulation of the motion of a single drop in a shear flow at finite Reynolds numbers, Iranian Journal of Science and Technology, 33 (B5) (2009) 441–452.

    Google Scholar 

  13. A. Komrakova, O. Shardt, D. Eskin and J. J. Derksen, Lattice Boltzmann simulations of drop deformation and breakup in shear flow, International Journal of Multiphase Flow, 59 (2014) 24–43.

    Article  Google Scholar 

  14. S. Dabiri, J. Lu and J. G. Tryggvason, Transition between regimes of a vertical channel bubbly upflow due to bubble deformability, Physics of Fluids, 25 (10) (2013) 102110.

    Article  Google Scholar 

  15. M. Muradoglu and G. Tryggvason, Simulations of soluble surfactants in 3D multiphase flow, Journal of Computational Physics, 274 (2014) 737–757.

    Article  MATH  Google Scholar 

  16. T. Kekesi, G. Amberg and L. P. Wittberg, Drop deformation and breakup in flows with shear, Chemical Engineering Science, 140 (2016) 319–329.

    Article  Google Scholar 

  17. A. Nourbakhsh and M. Shadmani, A study of the motion of a bubble in a combined Couette-Poiseuille flow using ANN and ANFIS: Effect of the Reynolds number, Journal of Fundamental and Applied Sciences, 8 (2S) (2016) 2306–2325.

    Google Scholar 

  18. S. N. Beesabathuni, S. E. Lindberg, M. Caggioni, C. Wesner and A. Q. Shen, Getting in shape: Molten wax drop deformation and solidification at an immiscible liquid interface, Journal of Colloid and Interface Science, 445 (2015) 231–242.

    Article  Google Scholar 

  19. W. Mao and A. Alexeev, Motion of spheroid particles in shear flow with inertia, Journal of Fluid Mechanics, 749 (2014) 145–166.

    Article  Google Scholar 

  20. T. Rosen, M. Do-Quang, C. K. Aidun and F. Lundell, Effect of fluid and particle inertia on the rotation of an oblate spheroidal particle suspended in linear shear flow, Physical Review E, 91 (2015) 053017.

    Article  Google Scholar 

  21. S. O. Unverdi and G. Tryggvason, Computations of multifluid flows, Physics, D60 (1992) 70–83.

    MATH  Google Scholar 

  22. S. O. Unverdi and G. Tryggvason, A front-tracking method for viscous incompressible multi-fluid flows, Journal of Computational Physics, 100 (1992) 25–37.

    Article  MATH  Google Scholar 

  23. M. Bayareh and S. Mortazavi, Effect of density ratio on the hydrodynamic interaction between two drops in simple shear flow, Iranian Journal of Science and Technology, 35 (M2) (2011) 121–132.

    MATH  Google Scholar 

  24. M. Bayareh and S. Mortazavi, Equilibrium position of a buoyant drop in Couette and Poiseuille flows at finite Reynolds numbers, Journal of Mechanics, 29 (1) (2013) 53–58.

    Article  Google Scholar 

  25. J. Feng, H. H. Hu and D. D. Joseph, Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part2. Couette and Poiseuille flows, Journal of Fluid Mechanics, 277 (1994) 271–301.

    Article  MATH  Google Scholar 

  26. J. S. Halow and G. B. Wills, Radial migration of spherical particles in couette systems, AIChE Journal, 16 (1970) 281–286.

    Article  Google Scholar 

  27. J. M. Rallison, A numerical study of the deformation and burst of a viscous drop in general shear flows, Journal of Fluid Mechanics, 109 (1981) 465–482.

    Article  MATH  Google Scholar 

  28. E. A. Ervin and G. Tryggvason, The rise of bubbles in a vertical shear flow, Journal of Fluids Engineering, 119 (1997) 443–449.

    Article  Google Scholar 

  29. P. C. H. Chan and L. G. Leal, The motion of a deformable drop in a second-order fluid, Journal of Fluid Mechanics, 92 (1979) 131–170.

    Article  MATH  Google Scholar 

  30. J. Li, Y. Y. Renardy and M. Renardy, Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method, Physics of Fluids, 12 (2000) 269–282.

    Article  MATH  Google Scholar 

  31. A. Karnis, H. L. Goldsmith and S. G. Mason, The kinetics of flowing dispersions. I. Concentrated suspensions of rigid particles, Journal of Colloid and Interface Science, 22 (1966) 531–553.

    Article  Google Scholar 

  32. J. K. Suh, Experimental and theoretical approaches on the burning behaviors of single n-heptane droplet, Journal of Mechanical Science and Technology, 29 (5) (2015) 2249–2257.

    Article  Google Scholar 

  33. H. Ban and G. Son, Numerical simulation of droplet evaporation between two circular plates, Journal of Mechanical Science and Technology, 29 (6) (2015) 2401–2407.

    Article  Google Scholar 

  34. K. Ha and K. Y. Han, Squeezing of resin droplet with various viscosities between two parallel glasses with very narrow gap, Journal of Mechanical Science and Technology, 29 (8) (2015) 3257–3265.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, Shahrekord University, Shahrekord, 8815648456, Iran

    Parisa Armandoost, Morteza Bayareh & Afshin Ahmadi Nadooshan

Authors
  1. Parisa Armandoost
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Morteza Bayareh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Afshin Ahmadi Nadooshan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Morteza Bayareh.

Additional information

Recommended by Associate Editor Seongwon Kang

Morteza Bayareh is a faculty member at Shahrekord University, Iran. He received his doctor degree in mechanical engineering from Isfahan University of Technology.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Armandoost, P., Bayareh, M. & Nadooshan, A.A. Study of the motion of a spheroidal drop in a linear shear flow. J Mech Sci Technol 32, 2059–2067 (2018). https://doi.org/10.1007/s12206-018-0415-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-018-0415-2

Keywords

Search

Navigation