We show how existing models for the sedimentation of monodisperse
flocculated suspensions and of polydisperse
suspensions of rigid spheres differing in size can be combined to yield a new
theory of the sedimentation processes of polydisperse
suspensions forming compressible sediments ("sedimentation with
compression"' or "sedimentation-consolidation process"). For N
solid particle species, this theory reduces in one space dimension to an
$N\times N$ coupled system of quasi-linear degenerate convection-diffusion
equations. Analyses of the characteristic polynomials of the Jacobian of the convective flux vector and of the diffusion
matrix show that this system is of strongly degenerate parabolic-hyperbolic
type for arbitrary N and particle size distributions. Bounds for the eigenvalues of both matrices are derived. The mathematical
model for N=3$ is illustrated by a numerical simulation obtained by the Kurganov-Tadmor central difference scheme for
convection-diffusion problems. The numerical scheme exploits the derived bounds
on the eigenvalues to keep the numerical diffusion to
a minimum.