Inertial confinement fusion fuel suffers increased x-ray radiation losses when carbon from the capsule ablator mixes into the hot-spot. Here, we present one- and two-dimensional ion Vlasov-Fokker-Planck simulations that resolve hot-spot self-heating in the presence of a localized spike of carbon mix, totalling 1.9% of the hot-spot mass. The mix region cools and contracts over tens of picoseconds, increasing its α particle stopping power and radiative losses. This makes a localized mix region more severe than an equal amount of uniformly distributed mix. There is also a purely kinetic effect that reduces fusion reactivity by several percent, since faster ions in the tail of the distribution are absorbed by the mix region. Radiative cooling and contraction of the spike induces fluid motion, causing neutron spectrum broadening. This artificially increases the inferred experimental ion temperatures and gives line of sight variations.