Advertisement

Experiments in Fluids

, Volume 50, Issue 5, pp 1293–1303 | Cite as

Dynamical deformation of a flat liquid–liquid interface

  • Nicolas DietrichEmail author
  • Souhila Poncin
  • Huai Z. Li
Research Article

Abstract

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo 1/Mo 2 ∈ [2 × 10−5–5 × 104] and Re 1/Re 2 ∈ [2 × 10−3–5 × 102].

Keywords

Particle Image Velocimetry Interfacial Tension Liquid Interface Viscosity Ratio Light Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

d

Diameter of the sphere, m

g

Gravity acceleration, ms−2

hmax

Height of fluid entrained behind the particle, m

R

Radius of the sphere, m

tc

Characteristic time of the sphere in the light liquid, s

tp

Time of passage of the sphere to cross the interface, s

ρ

Density, kg m−3

σ

Interfacial tension, N m−1

U

Terminal falling velocity of sphere, m s−1

Bo

=R 2Δρg/σ 12 Modified Bond number

Re

=ρud/μ, Reynolds number

Mo

=gμ C 4 /ρ C σ 3, Morton number

Subscripts

1

Initial phase met by the sphere (bubble)

2

Second phase met by the sphere (bubble) after the interface deformation

Notes

Acknowledgments

The financial assistance provided by the French Ministère de l’Enseignement Supérieur et de la Recherche is gratefully acknowledged.

References

  1. Bataille J, Lance M, Marie JL (1991). Some aspect of the modelling of bubbly flows. In: Hewitt GF, Mayinger F, Riznic JR (ed) Phase-interface phenomena in multiphase flow, pp 179–193Google Scholar
  2. Chateau X, Pitois O (2003) Quasistatic detachment of a sphere from a liquid interface. J Colloid Interf Sci 259:346–353CrossRefGoogle Scholar
  3. Chen JD, Hahn PS, Slattery JC (1984) Coalescence time for a small drop or bubble at a fluid-fluid interface. AICHE J 30:622–630CrossRefGoogle Scholar
  4. Chhabra RP, Tiu C, Uhlherr PHT (1981) Creeping motion of spheres through Ellis model fluids. Rheol Acta 20:346–351CrossRefGoogle Scholar
  5. Clift R, Grace JR, Weber ME (1978) Bubbles, drops et particles. Academic press, New YorkGoogle Scholar
  6. Danov KD, Gurkov TD, Raszillier H, Durst F (1998) Stokes flow caused by the motion of a rigid sphere close to a viscous interface. Chem Eng Sci 53:3413–3434CrossRefGoogle Scholar
  7. Dietrich N, Poncin S, Pheulpin S, LI HZ (2008) Passage of a bubble through a liquide-liquide interface. AICHE J 54(3):594–600CrossRefGoogle Scholar
  8. Frank X, Funfschilling D, Midoux N, Li HZ (2006) Bubbles in a viscous liquid: Lattice Boltzmann simulation and experimental validation. J Fluid Mech 546:113–122CrossRefzbMATHGoogle Scholar
  9. Geller AS, Lee SH, Leal LG (1986) The creeping motion of a spherical particle normal to a deformable interface. J Fluid Mech 169:27–69CrossRefzbMATHGoogle Scholar
  10. Harrison GM, Lawson NJ, Boger DV (2001) The measurement of the flow around a sphere settling in a rectangular box using 3-dimensional particle image velocimetry. Chem Eng Commun 188:143–178CrossRefGoogle Scholar
  11. Hartland S (1968) The approach of a rigid sphere to a deformable liquid/liquid interface. J Colloid Interf Sci 26:383–394CrossRefGoogle Scholar
  12. Jones AF, Wilson SDR (1978) The film drainage problem in droplet coalescence. J Fluid Mech 87:263–288CrossRefzbMATHGoogle Scholar
  13. Kemiha M, Olmos E, Fei W, Poncin S, Li HZ (2007) Passage of a gas bubble through a liquid-liquid interface. Ind Eng Chem Res 46:6099–6104CrossRefGoogle Scholar
  14. Lin CY, Slattery JC (1982) Thinning of a liquid film as a small drop or bubble approaches a fluid-fluid interface. AICHE J 28:792–798Google Scholar
  15. Maru HC, Wasan DT, Kintner RC (1971) Behavior of a rigid sphere at a liquid-liquid interface. Chem Eng Sci 26:1615–1628CrossRefGoogle Scholar
  16. Mena B, Manero O, Leal LG (1987) The influence of rheological properties on the slow flow past spheres. J Non-Newtonian Fluid Mech 26:247–275CrossRefGoogle Scholar
  17. Mohamed-Kassim Z, Longmire EK (2004) Drop coalescence through a liquid/liquid interface. Phys Fluids 16:2170–2181CrossRefGoogle Scholar
  18. Pitois O, Moucheront P, Weill C (1999) Franchissement d’interface et enrobage d’une sphère. Comptes Rendus de l’Académie des Sci Series IIB Mech Phys Astronomy 327:605–611CrossRefGoogle Scholar
  19. Satoh M, Aoki K, Chen J (2008) Electrically driven motion of an air bubble on hemispherical oil/water interface by three-phase boundary reactions. Langmuir 24:4364–4369CrossRefGoogle Scholar
  20. Tatuma JA, Finnisb MV, Lawsonc NJ, Harrisona GM (2005) 3D particle image velocimetry of the flow field around a sphere sedimenting near a wall Part 1. Effects of Weissenberg number. J Non-Newtonian Fluid Mech 141:99–115CrossRefGoogle Scholar
  21. Tirtaatmadja V, Uhlherr PHT, Sridhar T (1990) Creeping motion of spheres in fluid. J Non-Newtonian Fluid Mech 35:327–337CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Nicolas Dietrich
    • 1
    • 2
    Email author
  • Souhila Poncin
    • 1
  • Huai Z. Li
    • 1
  1. 1.Laboratory of Reactions and Process EngineeringNancy-Université, CNRSNancyFrance
  2. 2.Laboratoire d’Ingénierie des Systèmes Biologiques et des ProcédésUniversité de Toulouse, INSA, INRA-CNRSToulouseFrance

Personalised recommendations