Equation of mass balance and equation of particles
balance
Two independent functions of state are introduced: density of
particles and mass density (2002) [1 - 3]. Such division is
important, for example, when the material tends to a
fragmentation, as in this case the weight is preserved, but the
number of particles changes. Permeability of bodies is determined
by the density of particles, and internal interactions are
connected with the mass density. Introduction of the function of
distribution of particles, in essence, removes the border between
discrete and continuous media. Two independent equations are
formulated: the equation of mass balance and the equation of
balance of particles. A function determining the speed of new
particles creation appears in the equation of particles balance;
this function in its physical sense can be identified with the
chemical potential. The equation of energy balance also contains
terms which describe formation of new particles or fragmentation
of original particles.
- Zhilin P.A. Phase Transitions and General Theory of Elasto-Plastic Bodies // Proceedings of XXIX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia. 2002. P. 36-48.
- Zhilin P.A. Mathematical theory of non-elastic media // Uspehi
mechaniki (Advances in mechanics). Vol. 2. N 4. 2003. P. 3-36. (In Russian.)
- Zhilin P.A. On the general theory of non-elastic media // Mechanics of materials and strength of constructions.
Proc. of St. Petersburg State Polytechnical University.
N 489. 2004. P. 8-27. (In Russian.)