  We study the dynamics of interacting superfluid bosons in a one dimensional
vertical optical lattice after a sudden increase of the lattice potential
depth. We show that this system can be exploited to investigate the effects of
strong interactions on Bloch oscillations. We perform theoretical modelling of
this system, identify experimental challenges and explore a new regime of Bloch
oscillations characterized by interaction-induced matter-wave collapse and
revivals which modify the Bloch oscillations dynamics. In addition, we study
three dephasing mechanisms: effective three-body interactions, finite value of
tunneling, and a background harmonic potential. We also find that the center of
mass motion in the presence of finite tunneling goes through collapse and
revivals, giving an example of quantum transport where interaction induced
revivals are important. We quantify the effects of residual harmonic trapping
on the momentum distribution dynamics and show the occurrence of
interaction-modified temporal Talbot effect. Finally, we analyze the prospects
and challenges of exploiting Bloch oscillations of cold atoms in the strongly
interacting regime for precision measurement of the gravitational acceleration
$g$.
