A first order phase transition at high baryon density implies that a mixed
phase can occupy a significant region of the interior of a neutron star. In
this article, we investigate the effect of a droplet phase on neutrino tra
nsport inside the core. Two specific scenarios of the phase transition, one
having a kaon condensate and the other having quark matter in the high den
sity phase, are examined. The coherent scattering of neutrinos off the drop
lets greatly increases the neutrino opacity of the mixed phase. We comment
on how the existence of such a phase will affect a supernova neutrino signa
l. (C) 2000 Elsevier Science B.V. All rights reserved.