Skip to main content
SpringerLink
Log in

An experimental investigation on inertia motion and deformation of Boger drops falling through Newtonian media

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

In the present study, deformations and drag coefficients of viscoelastic drops (Boger drops) with different elasticity falling into the air and oil are investigated experimentally. The main object of the present study is an evaluation of the fluid elasticity effects on drop dynamics by comparing the results with Newtonian cases (water, ethanol and aqueous solution of sodium dodecyl benzene sulfonate). A CMOS high-speed camera is used to capture images of falling drops and the cinematic calculations are performed using image processing. Here, a theoretical correlation is presented to describe the drag coefficient as a function of Reynolds number based on Newton’s second-law. In addition, effects of viscosity ratio (\( k \)), elasticity number (\( En \)) and Bond number (\( Bo \)) on the drag coefficient are studied. The results express that the drag coefficient increases by increasing viscosity ratio. For drops with the same viscosities, by increasing elasticity number and reducing Bond number, the drag coefficient is enhanced. It is also observed that the deformation of Newtonian drops falling in the air is periodic. These oscillations are caused by the interaction between surface tension forces and hydrodynamic pressure and the presence of internal circulation flows leading to instability on the surface of droplets. The amplitude oscillation for viscoelastic drops is remarkably lower than Newtonian drops. By increasing the viscosity of exterior fluid (when drops fall in the oil), periodic deformation of Newtonian drops is gradually damped and spherical drops are changed to elliptical ones. These changes are also observed for viscoelastic droplets.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Bäumler K, Wegener M, Paschedag A, Bänsch E (2011) Drop rise velocities and fluid dynamic behavior in standard test systems for liquid/liquid extraction—experimental and numerical investigations. Chem Eng Sci 66:426–439

    Article  Google Scholar 

  2. Ohta M, Iwasaki E, Obata E, Yoshida Y (2003) A numerical study of the motion of a spherical drop rising in shear-thinning fluid systems. J Nonnewton Fluid Mech 116:95–111

    Article  MATH  Google Scholar 

  3. Megias-Alguacil D, Feigl K, Dressler M, Fischer P, Windhab E (2005) Droplet deformation under simple shear investigated by experiment, numerical simulation and modeling. J Nonnewton Fluid Mech 126:153–161

    Article  MATH  Google Scholar 

  4. Liu L, Tang H, Quan S (2013) Shapes and terminal velocities of a drop rising in stagnant liquids. Comput Fluids 81:17–25

    Article  Google Scholar 

  5. Sideman S, Taitel Y (1964) Direct-contact heat transfer with change of phase: evaporation of drops in an immiscible liquid medium. Int J Heat Mass Transf 7:1275–1289

    Article  Google Scholar 

  6. Sideman S, Gat Y (1966) Direct contact heat transfer with change of phase: spray-column studies of a three-phase heat exchanger. AIChE J 12:296–303

    Article  Google Scholar 

  7. Taylor G (1934) The formation of emulsions in definable fields of flow. Proc R Soc Lond Ser A Contain Pap Math Phys Character 146:501–523

    Article  ADS  Google Scholar 

  8. Rallison J (1981) Numerical study of the deformation and burst of a viscous drop in general shear flows. J Fluid Mech 109:465–482

    Article  ADS  MATH  Google Scholar 

  9. Bentley B, Leal L (1986) Computer-controlled four-roll mill for investigations of particle and drop dynamics in two-dimensional linear shear flows. J Fluid Mech 167:219–240

    Article  ADS  MATH  Google Scholar 

  10. Wairegi T, Grace J (1976) The behaviour of large drops in immiscible liquids. Int J Multiph Flow 3:67–77

    Article  Google Scholar 

  11. Taylor T, Acrivos A (1964) On the deformation and drag of a falling viscous drop at low Reynolds number. J Fluid Mech 18:466–476

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Feng JQ, Beard KV (2011) Raindrop shape determined by computing steady axisymmetric solutions for Navier–Stokes equations. Atmos Res 101:480–491

    Article  Google Scholar 

  13. Helenbrook B, Edwards C (2002) Quasi-steady deformation and drag of uncontaminated liquid drops. Int J Multiph Flow 28:1631–1657

    Article  MATH  Google Scholar 

  14. Bozzi LA, Feng JQ, Scott TC, Pearlstein AJ (1997) Steady axisymmetric motion of deformable drops falling or rising through a homoviscous fluid in a tube at intermediate Reynolds number. J Fluid Mech 336:1–32

    Article  ADS  MATH  Google Scholar 

  15. Dandy DS, Leal LG (1989) Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers. J Fluid Mech 208:161–192

    Article  ADS  Google Scholar 

  16. Magarvey R, Taylor B (1956) Free fall breakup of large drops. J Appl Phys 27:1129

    Article  ADS  Google Scholar 

  17. Arecchi F, Buah-Bassuah P, Francini F, Residori S (1996) Fragmentation of a drop as it falls in a lighter miscible fluid. Phys Rev E 54:424

    Article  ADS  Google Scholar 

  18. Graham D, Higdon J (2000) Oscillatory flow of droplets in capillary tubes. Part 2. Constricted tubes. J Fluid Mech 425:55–77

    Article  ADS  MATH  Google Scholar 

  19. Baumann N, Joseph DD, Mohr P, Renardy Y (1993) Vortex rings of one fluid in another in free fall. Phys Fluids 4:567

    Article  ADS  Google Scholar 

  20. Ni MJ, Komori S, Morley NB (2006) Direct simulation of falling droplet in a closed channel. Int J Heat Mass Transf 49:366–376

    Article  MATH  Google Scholar 

  21. Fakhari A, Rahimian MH (2011) Investigation of deformation and breakup of a falling droplet using a multiple-relaxation-time lattice Boltzmann method. Comput Fluids 40:156–171

    Article  MATH  Google Scholar 

  22. Tilehboni S, Sedighi K, Farhadi M, Fattahi E (2013) Lattice Boltzmann simulation of deformation and breakup of a droplet under gravity force using interparticle potential model. Int J Eng Trans A Basics 26:781–794

    Google Scholar 

  23. Wegener M, Kraume M, Paschedag AR (2010) Terminal and transient drop rise velocity of single toluene droplets in water. AIChE J 56:2–10

    Google Scholar 

  24. Mukherjee S, Sarkar K (2011) Viscoelastic drop falling through a viscous medium. Phys Fluids 23:013101

    Article  ADS  Google Scholar 

  25. Smagin I, Pathak M, Lavrenteva OM, Nir A (2011) Motion and shape of an axisymmetric viscoplastic drop slowly falling through a viscous fluid. Rheol Acta 50:361–374

    Article  Google Scholar 

  26. German G, Bertola V (2010) The free-fall of viscoplastic drops. J Nonnewton Fluid Mech 165:825–828

    Article  Google Scholar 

  27. Sostarecz MC, Belmonte A (2003) Motion and shape of a viscoelastic drop falling through a viscous fluid. J Fluid Mech 497:235–252

    Article  ADS  MATH  Google Scholar 

  28. Wanchoo R, Sharma SK, Gupta R (2003) Shape of a Newtonian liquid drop moving through an immiscible quiescent non-Newtonian liquid. Chem Eng Process 42:387–393

    Article  Google Scholar 

  29. Li H, Sundararaj U (2010) Experimental investigation of viscoelastic drop deformation in Newtonian matrix at high capillary number under simple shear flow. J Nonnewton Fluid Mech 165:1219–1227

    Article  Google Scholar 

  30. Kishore N, Chhabra R, Eswaran V (2007) Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers. Chem Eng Sci 62:2422–2434

    Article  Google Scholar 

  31. Winnikow S, Chao B (1966) Droplet motion in purified systems. Phys Fluids 9:50

    Article  ADS  Google Scholar 

  32. Becker E, Hiller W, Kowalewski T (1991) Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets. J Fluid Mech 231:189–210

    Article  ADS  MATH  Google Scholar 

  33. Kleinstreuer C, Feng Y (2013) Computational analysis of non-spherical particle transport and deposition in shear flow with application to lung aerosol dynamics—a review. J Biomech Eng 135:021008

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    M. Norouzi, H. Abdolnezhad & S. Mandani

Authors
  1. M. Norouzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Abdolnezhad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Mandani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Norouzi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (MP4 216 kb)

Supplementary material 2 (MP4 216 kb)

Supplementary material 3 (MP4 690 kb)

Appendix

Appendix

figure a
figure b
figure c

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Norouzi, M., Abdolnezhad, H. & Mandani, S. An experimental investigation on inertia motion and deformation of Boger drops falling through Newtonian media. Meccanica 54, 473–490 (2019). https://doi.org/10.1007/s11012-019-00961-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-019-00961-0

Keywords

Search

Navigation