Investigation of wave propagation velocities in fluid mixtures

L. A. Molotkov

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 35, Tome 332 (2006), pp. 149-162

Résumé

In order to determine the wave propagation velocities in the fluid mixtures, the mixtures are approximated by block structures. These structures consist of the same cells containing eight blocks. The pointed out blocks can be filled by different fluids. In the block structures we carry out the passage to the limit under conditions that sizes of blocks tend to zero but relative sizes of blocks remain constant. In common case the average wave field satisfies equations of anisotropy fluids. We consider two partial cases of mixtures of two fluids. In the first case, both fluids are intermixed completely. In the second case, there are periodic inclusions with one fluid into other fluid. In both cases, the fluid mixtures are homogeneous isotropic and the formulas for velocities are obtained. These formulas determine dependence of the velocities on percentage composition and on parameters of two mixed fluid. The velocity of propagation in a fluid mixture cannot be greater than the greatest velocity but can be less than the least velocity in mixed fluids.