The axisymmetric, dynamic breakup of a Newtonian liquid jet injected v
ertically into another immiscible Newtonian liquid at various Reynolds
numbers is investigated here. The full transient from jet start-up to
breakup into drops was simulated numerically by solving the time-depe
ndent axisymmetric equations of motion and continuity using an algorit
hm based on the Volume of Fluid (VOF) method that was previously prove
n successful in simulations of steady-state liquid jets (i.e., of the
jet region close to the nozzle before breakup). The algorithm has been
further refined here based on its performance on transient problems s
uch as the solution of the free liquid-liquid capillary jet breakup pr
oblem. The comparison of the simulation results with previous experime
ntal measurements of jet length under conditions where all forces, i.e
., viscous, inertial, buoyancy, and surface tension, are important, ca
n be judged satisfactory given the sensitive dependence of the results
on details of the experimental setup that are not available. The comp
arison involves the jet length till breakup as well as the jet and dro
p shapes, often far from regular. In comparison with experiment, the r
esults of the present numerical method show a greater sensitivity of t
he jet length to the Reynolds number than the best predictions previou
sly available based on the linear stability analysis of the free liqui
d-liquid capillary jet breakup problem.