  The phase separation of a simple binary mixture of incompatible linear
polymers in solution is investigated using an extension of the sedimentation
equilibrium method, whereby the osmotic pressure of the mixture is extracted
from the density profiles of the inhomogeneous mixture in a gravitational
field. In Monte-Carlo simulations the field can be tuned to induce significant
inhomogeneity, while keeping the density profiles sufficiently smooth for the
macroscopic condition of hydrostatic equilibrium to remain applicable. The
method is applied here for a simplified model of ideal, but mutually avoiding
polymers, which readily phase separate at relatively low densities. The
Monte-Carlo data are interpreted with the help of an approximate bulk phase
diagram calculated from a simple, second order virial coefficient theory. By
deriving effective potentials between polymer centres of mass, the binary
mixture of polymers is coarse-grained to a ``soft colloid'' picture reminiscent
of the Widom-Rowlinson model for incompatible atomic mixtures. This approach
significantly speeds up the simulations, and accurately reproduces the
behaviour of the full monomer resolved model.
