  A computational framework is developed to address capillary self-focusing in
Step Emulsification. The microfluidic system consists of a single shallow and
wide microchannel that merges into a deep reservoir. A continuum approach
coupled with a volume of fluid method is used to model the capillary
self-focusing effect. The original governing equations are reduced using the
Hele-Shaw approximation. We show that the interface between the two fluids
takes the shape of a neck narrowing in the flow direction just before entering
the reservoir, in agreement with our experimental observations. Our
computational model relies on the assumption that the pressure at the boundary,
where the fluid exits into the reservoir, is the uniform pressure in the
reservoir. We investigate this hypothesis by comparing the numerical results
with experimental data. We conjecture that the pressure boundary condition
becomes important when the width of the neck is comparable to the depth of the
microchannel. A correction to the exit pressure boundary condition is then
proposed, which is determined by comparison with experimental data. We also
present the experimental observations and the numerical results of the
transitions of breakup regimes.
