Here we study the dynamics of a bubble or drop as it is driven by a pr
essure gradient through a capillary tube. For the case or a straight c
apillary, the drop can either approach a steady-state shape or the rea
r of the drop develops a re-entrant cavity. Also, depending on the ini
tial conditions, the drop can break apart into smaller drops. For flow
through a constricted capillary tube, depending on the physical param
eters of the problem, the drop can either move through the constrictio
n or break into two or more pieces as it moves past the constriction.
We study this snap-off process numerically and determine the effect of
the physical parameters on the dynamics of the drop.