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Dynamical deformation of a flat liquid–liquid interface

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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].

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Abbreviations

d :

Diameter of the sphere, m

g :

Gravity acceleration, ms−2

h max :

Height of fluid entrained behind the particle, m

R :

Radius of the sphere, m

t c :

Characteristic time of the sphere in the light liquid, s

t p :

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 4 C /ρ C σ 3, Morton number

1:

Initial phase met by the sphere (bubble)

2:

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

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Acknowledgments

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

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Authors and Affiliations

  1. Laboratory of Reactions and Process Engineering, Nancy-Université, CNRS, 1 rue Grandville, 54000, Nancy, France

    Nicolas Dietrich, Souhila Poncin & Huai Z. Li

  2. Laboratoire d’Ingénierie des Systèmes Biologiques et des Procédés, Université de Toulouse, INSA, INRA-CNRS, 135 avenue de Rangueil, 31077, Toulouse, France

    Nicolas Dietrich

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  1. Nicolas Dietrich
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  2. Souhila Poncin
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Correspondence to Nicolas Dietrich.

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Dietrich, N., Poncin, S. & Li, H.Z. Dynamical deformation of a flat liquid–liquid interface. Exp Fluids 50, 1293–1303 (2011). https://doi.org/10.1007/s00348-010-0989-7

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