Small oscillations of an emulsion of two weakly viscous compressible liquids

The small oscillations of an emulsion of two weakly viscous compressible liquids in an external acoustic field are studied. The structure of the mixture is assumed to be periodic with a sufficiently by small cell size. An integro-differential acoustic equation and an expression for the mean velocity are derived by the two-scale convergence method and the strong convergence of the difference in the velocities and the difference in the velocity gradients of the prelimiting and limiting problems (the initial problem and the averaged problem) to zero in L2 is proved. The elements of the dynamic “filtration matrix”, that is, of the kernel of the convolution of the acoustic equation, are calculated by the finite volume methods.