Hua, J., Stene, J.F. and Lin, P. (2008) Numerical Simulation of 3D Bubbles Rising in Viscous Liquids Using a Front Tracking Method. Journal of Computational Physics, 227, 3358-3382.
http://dx.doi.org/10.1016/j.jcp.2007.12.002

has been cited by the following article:

• TITLE: Numerical Simulation of Single Bubble Deformation in Straight Duct and 90° Bend Using Lattice Boltzmann Method

  AUTHORS: Hamid Mohammad Mirzaie Daryan, Mohammad Hasan Rahimian

  KEYWORDS: Bubble Deformation, Straight Duct, 90° Bend, Lattice Boltzmann Method, Curved Wall Boundary Condition, Deformation Benchmark

  JOURNAL NAME: Journal of Electronics Cooling and Thermal Control, Vol.5 No.4, December 15, 2015

  ABSTRACT: The paper aims to give a comprehensive investigation of the two dimensional deformation of a single bubble in a straight duct and a 90° bend under the zero gravity condition. For this, the two phase flow lattice Boltzmann equation (LBE) model is used. An averaging scheme of boundary condition implementation has been applied and validated. A generalized deformation benchmark has been introduced. By presenting and analyzing the shape of the bubbles moving through the channels, the effects of the all important nondimensional numbers on the bubble deformation are examined thoroughly. It is seen that by increasing the Weber number the rate of the deformation enhances. Besides, because of the velocity dissimilarity between the particles constructing the bubble, the initial coordinates and the diameter of the bubble play a great role in the future behavior of the bubble. The density ratio has a little effect on the shape of the bubble within the assumed range of the density ratio. Moreover, as the Reynolds number or the viscosity ratio is decreased, higher rate of deformation is exhibited. Finally it is found that there is an inverse proportionality between the amplitude and frequency of the bubble deformation.