  We consider a simple generic dissipative dark matter model: a hidden sector
featuring two dark matter particles charged under an unbroken $U(1)'$
interaction. Previous work has shown that such a model has the potential to
explain dark matter phenomena on both large and small scales. In this
framework, the dark matter halo in spiral galaxies features nontrivial
dynamics, with the halo energy loss due to dissipative interactions balanced by
a heat source. Ordinary supernovae can potentially supply this heat provided
kinetic mixing interaction exists with strength $\epsilon \sim 10^{-9}$. This
type of kinetically mixed dark matter can be probed in direct detection
experiments. Importantly, this self-interacting dark matter can be captured
within the Earth and shield a dark matter detector from the halo wind, giving
rise to a diurnal modulation effect. We estimate the size of this effect for
detectors located in the Southern hemisphere, and find that the modulation is
large ($\gtrsim 10\%$) for a wide range of parameters.
