  We combine a heuristic theory of geometric percolation and the Smoluchowski
theory of colloid dynamics to predict the impact of shear flow on the
percolation threshold of hard spherical colloidal particles, and verify our
findings by means of molecular dynamics simulations. It appears that the impact
of shear flow is subtle and highly non-trivial, even in the absence of
hydrodynamic interactions between the particles. The presence of shear flow can
both increase and decrease the percolation threshold, depending on the
criterion used for determining whether or not two particles are connected and
on the P\'{e}clet number. Our approach opens up a route to quantitatively
predict the percolation threshold in nanocomposite materials that, as a rule,
are produced under non-equilibrium conditions, making comparison with
equilibrium percolation theory tenuous. Our theory can be adapted
straightforwardly for application in other types of flow field, and particles
of different shape or interacting via other than hard-core potentials.
