Migration of a van der Waals bubble: Lattice Boltzmann formulation

D. J. Holdych, J. G. Georgiadis, R. O. Buckius

Research output: Contribution to journalArticlepeer-review


A numerical study of the isothermal migration of a two-dimensional bubble in Poiseuille flow is reported here for vapor-liquid density and dynamic viscosity ratios of 1/8, Red=1, and Ca=2. A lattice Boltzmann model with a van der Waals equation of state is employed to simulate the diffuse interface for three interface thickness to bubble diameter ratios, 1/5, 1/10, and 1/20. Point-by-point comparisons with the sharp-interface incompressible counterpart (reported in the literature) reveal velocity discrepancies which are more evident on the vapor side. These differences are a manifestation of a finite mass flux through the interface, associated with driven finite-thickness interfaces. An analytical study of the one-dimensional analog of the traveling diffuse interface problem explains this phenomenon and shows that this flux vanishes as a result of viscous dissipation as the interface thickness tends to zero. This trend is corroborated by the two-dimensional lattice Boltzmann results.

Original languageEnglish (US)
Pages (from-to)817-825
Number of pages9
JournalPhysics of fluids
Issue number4
StatePublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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