Geodesic
On attenuation of waves propagating in fluid mixtures
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 148-179

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Wave propagation in fluid mixtures is investigated on the basis of effective models of block and layer media. These models are anisotropic fluids described by wave equations. In the pointed out equations, additional terms describing wave attenuation are introduced. This attenuation is connected with friction force proporitional to difference of tangent displacements on boundaries. In consequence of the attenuation the total energy of the wave field decreases steadly and amplitudes of the waves reduce with time by expotential law. This law of descreasing is determined by attenuation coefficients. The mentioned attenuation coefficients is determined in the two cases, that two fluids are mixed thoroughly and that the particles of one fluid are inclusions into another fluid. The suggested approach permits to consider also more complicated fluid mixtures. 
@article{ZNSL_2005_324_a9,
     author = {L. A. Molotkov},
     title = {On attenuation of waves propagating in fluid mixtures},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {148--179},
     publisher = {mathdoc},
     volume = {324},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a9/}
}
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L. A. Molotkov. On attenuation of waves propagating in fluid mixtures. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 34, Tome 324 (2005), pp. 148-179. http://geodesic.mathdoc.fr/item/ZNSL_2005_324_a9/