1. On balance laws for mixture theories with phase change Wolfgang Dreyer Frank Duderstadt Maren Hantke Gerald Warnecke WIAS Berlin Otto-von-Guericke-University Magdeburg Micro-Macro Modelling and Simulation of Liquid-Vapour Flows Strasbourg, January 2008

2. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Motivation Model phase transitions 2 separated phases - carrier phase - disperse phase 2-phase mixture balance laws involving phase change Averaging techniques NOW: close the system

3. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Multi-bubble system Single-bubble system 1D - case

4. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 A closed system under prescribed outer pressure, 1D-case p0p0 Assumptions: Ideal gas, inviscid Homogeneity in the gas Incompressible, inviscid liquid Vapour Liquid Interface Kinetic relation

5. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results Light blue: fixed temperatureLight blue: fixed temperaturegreen: IELight blue: fixed temperaturegreen: IEred: PDE

6. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 A closed system under prescribed outer pressure, radial symmetric case p0p0 Assumptions: Radial symmetry Ideal gas, inviscid Homogeneity in the gas Incompressible, inviscid liquid Interface Vapour Kinetic relation Liquid

7. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results Red: fixed temperatureRed: fixed temperaturegreen: PDE

8. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results, fixed initial radius Red: p0=1650 Pagreen: p0=1600 Palight blue: p0=1550 Pa

9. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Numerical results, fixed initial mass Red: p0=1650 Pagreen: p0=1600 Palight blue: p0=1550 Pa

10. Maren Hantke On balance laws for mixture theories with phase changeStrasbourg, January 2008 Future work Can we neglect the temperature differences caused by the phase transition? Close the averaged system of balance laws Investigate the droplet system