  Optical lattices offer the possibility to investigate the superfluid
properties of both Bose condensates and Fermionic superfluid gases. When a
population imbalance is present in a Fermi mixture, this leads to frustration
of the pairing, and the superfluid properties will be affected. In this
contribution, the influence of imbalance on the flow of a Fermi superfluid
through an optical lattice is investigated. The flow through the lattice is
analysed by taking into account coupling between neighbouring layers of the
optical lattice up to second order in the interlayer tunneling amplitude for
single atoms. The critical velocity of flow through the lattice is shown to
decrease monotonically to zero as the imbalance is increased to 100%.
Closed-form analytical expressions are given for the tunneling contribution to
the action and for the critical velocity as a function of the binding energy of
pairs in the (quasi) two-dimensional Fermi superfluid and as a function of the
imbalance.
