  As small solid grains grow into larger ones in protoplanetary nebulae, or in
the cloudy atmospheres of exoplanets, they generally form porous aggregates
rather than solid spheres. A number of previous studies have used highly
sophisticated schemes to calculate opacity models for irregular, porous
particles with size much smaller than a wavelength. However, mere growth itself
can affect the opacity of the medium in far more significant ways than the
detailed compositional and/or structural differences between grain constituents
once aggregate particle sizes exceed the relevant wavelengths. This physics is
not new; our goal here is to provide a model that provides physical insight and
is simple to use in the increasing number of protoplanetary nebula evolution,
and exoplanet atmosphere, models appearing in recent years, yet quantitatively
captures the main radiative properties of mixtures of particles of arbitrary
size, porosity, and composition. The model is a simple combination of effective
medium theory with small-particle closed-form expressions, combined with
suitably chosen transitions to geometric optics behavior. Calculations of
wavelength-dependent emission and Rosseland mean opacity are shown and compared
with Mie theory. The model's fidelity is very good in all comparisons we have
made, except in cases involving pure metal particles or monochromatic opacities
for solid particles with size comparable to the wavelength.
