| Abstract: | The linear hydrodynamic stability of the plane Couette flow of a suspension with a finite volume fraction of the particles
is considered. The two-phase medium flow is described within the framework of the model of mutually penetrating continua which
allows for the finiteness of the volume occupied by the particles. In the main flow the phase velocities are the same, while
gravity is not taken into account. The stability of disperse flows with both uniform and nonuniform particle distributions
is studied. The linearized system of the equations of suspension motion with the no-slip boundary conditions imposed on solid
walls is reduced to the eigenvalue problem for an ordinary differential fourth-order equation in the stream function. The
eigenvalues are sought using the orthogonolization method. The parametric investigation of the stability characteristics of
the disperse flow is performed. It is shown that in the case of the uniform spatial distribution of the particles in the main
flow, the presence of an admixture in the flow leads to a slight variation in the wave decay rates, while the flow remains
stable for any permissible combinations of the dimensionless governing parameters. In the case of nonuniform distribution
of inclusions the flow loses stability already for low Reynolds numbers on a wide range of the dimensionless governing parameters. |
