  The standard treatment of impurities in metals assumes a homogeneous
distribution of impurities. In this paper we study distributions that are
inhomogeneous. We discuss in detail the "isotropic inhomogeneous scattering
model" which takes into account the spatially varying scattering on the scale
of the superfluid coherence length. On a large scale the model reduces to a
homogeneous medium with renormalized parameter values. We apply the model to
superfluid 3He, where porous aerogel acts as the impurity. We calculate the
transition temperature Tc, the order parameter, and the superfluid density.
Both A- and B-like phases are considered. Two different types of behavior are
identified for the temperature dependence of the order parameter. We compare
the calculations with experiments on 3He in aerogel. We find that most of the
differences between experiments and the homogeneous theory can be explained by
the inhomogeneous model. All our calculations are based on the quasiclassical
theory of Fermi liquids. The parameters of this theory for superfluid 3He in
aerogel are discussed.
