Study of the rise of a single/multiple bubbles in quiescent liquids using the VOF method

  • Wassim Abbassi
  • Sonia BesbesEmail author
  • Habib Ben Aissia
  • Jean Yves Champagne
Technical Paper


In this paper, computational fluid dynamics was used to study the dynamics of a single and multiple bubbles in quiescent liquids using the volume of fluid method. The effect of liquid viscosity, bubbles size and initial bubbles configuration on the bubbles dynamics and interactions was investigated. It is found that the bubble rising trajectory changes from rectilinear to zigzag trajectory as liquid viscosity decreases. The different behaviors of bubbles introduce various liquid flow structures. For three bubbles rising side by side, the magnitude of bubble shape oscillations increases compared to the case of a single bubble. This is due to the fluctuations in liquid phase velocity fields which were induced by the liquid flow around the two neighboring bubbles. However, for two in-line bubbles with different sizes, the larger bubble always has a strong effect on the smaller one for each initial configuration.


Volume of fluid (VOF) method Two-phase flows Bubble dynamics Liquid flow structure Bubble interactions 

List of symbols


Bubble diameter (m)


Orifice diameter (m)


Bubble aspect ratio


Eötvös number (\( Eo = \left( {\rho_{\text{l}} - \rho_{\text{g}} } \right)gD_{\text{b}}^{2} /\sigma \))


Surface tension force (N/m3)


Gravity acceleration (m/s2)


Bubble height (m)


Local surface curvature


Exact curvature


Morton number (\( Mo = g\mu_{\text{l}}^{4} \Delta \rho /\rho_{\text{l}}^{2} \sigma^{3} \))

\( \hat{n} \)

Unit surface normal vector


Pressure (Pa)


Pressure difference between the inside and outside of the bubble (Pa)


Exact pressure jump (Pa)


Gas flow rate (m3/s)


Bubble radius (m)


Reynolds number (\( Re = \rho_{\text{l}} U_{\text{b}} D_{\text{b}} /\mu_{\text{l}} ) \)


Initial center-to-center separation distance (m)

\( S_{0}^{*} \)

Dimensionless initial separation distance (S0/Db)


Time (s)


Time interval between two sequences (s)


Time step (s)

\( \vec{u} \)

Velocity vector (m/s)


Bubble width (m)


Weber number (\( We = \rho_{l} U_{b}^{2} D_{b} /\sigma \))

X, Y

Cartesian coordinate (m)

Greek letters


Volume fraction (dimensionless)


Viscosity (Pa s)


Density (kg/m3)


Surface tension (N/m)







Gas phase


Liquid phase



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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  • Wassim Abbassi
    • 1
  • Sonia Besbes
    • 1
    Email author
  • Habib Ben Aissia
    • 1
  • Jean Yves Champagne
    • 2
  1. 1.Laboratory of Metrology and Energy Systems (LMES)National School of Engineers (ENIM)MonastirTunisia
  2. 2.Laboratory of Fluid Mechanics and Acoustics (LMFA)National Institute of Applied Science (INSA), LyonVilleurbanne CedexFrance

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