WIAS Preprint No. 1741, (2012)

On balance laws for mixture theories of disperse vapor bubbles in liquid with phase change


  • Dreyer, Wolfgang
  • Hantke, Maren
  • Warnecke, Gerald

2010 Mathematics Subject Classification

  • 35Q53 35G25 76E15


  • averaging methods, conservation laws, phase change, bubbles, phase mixtures




We study averaging methods for the derivation of mixture equations for disperse vapor bubbles in liquids. The carrier liquid is modeled as a continuum, whereas simplified assumptions are made for the disperse bubble phase. An approach due to Petrov and Voinov is extended to derive mixture equations for the case that there is a phase transition between the carrier liquid and the vapor bubbles in water. We end up with a system of balance laws for a multi-phase mixture, which is completely in divergence form. Additional non-differential source terms describe the exchange of mass, momentum and energy between the phases. The sources depend explicitly on evolution laws for the total mass, the radius and the temperature of single bubbles. These evolution laws are derived in a prior article and are used to close the system. Finally numerical examples are presented.

Appeared in

  • Continuum Mechanics and Thermodynamics, 26 (2014) pp. 521--549.

Download Documents