  Interactions in electron systems can lead to viscous flows in which
correlations allow electrons to avoid disorder scattering, reducing momentum
loss and dissipation. We illustrate this behavior in a viscous pinball model,
describing electrons moving in the presence of dilute point-like defects.
Conductivity is found to obey an additive relation
$\sigma=\sigma_0+\Delta\sigma$, with a non-interacting Drude contribution
$\sigma_0$ and a contribution $\Delta\sigma>0$ describing conductivity
enhancement due to interactions. The quantity $\Delta\sigma$ is enhanced by a
logarithmically large factor originating from the Stokes paradox at the
hydrodynamic lengthscales and, in addition, from an effect of repeated returns
to the same scatterer due to backreflection in the carrier-carrier collisions
occurring at the ballistic lengthscales. The interplay between these effects is
essential at the ballistic-to-viscous crossover.
