  We investigate the effect exerted by spin-polarized fermions on the
interaction between superfluid bosons for a Bose-Fermi mixture residing on an
optical lattice, with particular emphasis on the possibility of an induced
phase-separation. Using a set of microscopic parameters relevant to a
$^{40}$K-$^{87}$Rb mixture, we show how the phase-separation criterion may be
directly probed by means of the critical superfluid velocity of the bosonic
condensate. We report quantitative results for the magnitude of the superfluid
velocity and its dependence on the trap depth, the boson-fermion interaction,
and the fermionic filling fraction. All of these parameters can be controlled
experimentally in a well-defined manner. We propose an experimental setup for
probing the critical superfluid velocity.
