tailieunhanh - Phase change with voids and bubbles
The state variables are the temperature, the strain tensor, and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to microscopic motion responsible for the phase change). | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 3 &4 (2009), pp. 263 – 277 PHASE CHANGE WITH VOIDS AND BUBBLES Francesco Ascione, Michel Frémond Laboratorio Lagrange, Dipartimento di Ingegneria Civile, Università di Roma "Tor Vergata", Italy Abstract. We investigate phase transition at the macroscopic level. The main novelty of our approach is the possibility of having voids during the phase change. This aspect is described in the model by the mass balance equation which results in a pressure which has a paramount importance. The state variables are the temperature, the strain tensor, and the volume fractions of the two phases (whose evolutions are described by a vectorial equation coming from the principle of virtual power and related to microscopic motion responsible for the phase change). The theory accounts for the main physical phenomenons, for instance, for the cavitation phenomenon and for pressure dependance of the phase change temperature. The scope of the predictive theory is illustrated with uni-dimensional examples. 1. INTRODUCTION Bubbles or voids may appear in phase change. In the ice of a frozen pond, it may be seen very small bubbles. In cast iron voids or bubbles are present. In an ice-cream there are also voids which may influence its quality and even its taste. We address this phase change phenomenon at the macroscopic level and derive a predictive theory. We assume ~ = (β1 , β2 ), [2, 4]. The two phases do not there are two phase volume fractions β1 and β2 , β fill the whole volume. As for an example, we assume that β1 is the liquid volume fraction, water for instance, and β2 is the solid volume fraction, ice for instance. The voids volume fraction is = 1 − β1 − β2 . The predictive theory is presented in paragraphs 2 and 3 describing the equations of motion and the constitutive laws. Its properties are investigated in paragraph 4. The theory accounts for : the cavitation phenomenon where voids appear when pressure becomes negative in a .
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