  Patterned irradiation of cuprate superconductors with columnar defects allows
a new generation of experiments which can probe the properties of vortex
liquids by confining them to controlled geometries. Here we show that an
analysis of such experiments that combines an inhomogeneous Bose glass scaling
theory with the hydrodynamic description of viscous flow of vortex liquids can
be used to infer the critical behavior near the Bose glass transition. The
shear viscosity is predicted to diverge as $|T-T_{BG}|^{-z}$ at the Bose glass
transition, with $z\simeq 6$ the dynamical critical exponent.
