  The Casimir-Lifshitz force is calculated between two inhomogeneous composite
slabs, each made of a homogeneous matrix with spherical metallic inclusions.
The effective dielectric function of the slabs is calculated using several
effective medium approximations and we compare the resulting forces as a
function of slab separation and filling fraction. We show that the choice of
effective medium approximation is critical in making precise comparisons
between theory and experiment. The role that the spectral representation of the
effective medium plays in making a Wick rotation to the complex frequency axis
is also discussed.
