  The behavior of an oil droplet pinned at the entrance of a micropore and
subject to clossflow-induced shear is investigated numerically by solving the
Navier-Stokes equation. We found that in the absence of crossflow, the critical
transmembrane pressure required to force the droplet into the pore is in
excellent agreement with a theoretical prediction based on the Young-Laplace
equation. With increasing shear rate, the critical pressure of permeation
increases, and at sufficiently high shear rates the oil droplet breaks up into
two segments. The results of numerical simulations indicate that droplet
breakup at the pore entrance is facilitated at lower surface tension, higher
oil-to-water viscosity ratio and larger droplet size but is insensitive to the
value of the contact angle. Using simple force and torque balance arguments, an
estimate for the increase in critical pressure due to crossflow and the breakup
capillary number is obtained and validated for different viscosity ratios,
surface tension coefficients, contact angles, and drop-to-pore size ratios.
