The behavior of an oil droplet pinned at the entrance of a micropore andsubject to clossflow-induced shear is investigated numerically by solving theNavier-Stokes equation. We found that in the absence of crossflow, the criticaltransmembrane pressure required to force the droplet into the pore is inexcellent agreement with a theoretical prediction based on the Young-Laplaceequation. With increasing shear rate, the critical pressure of permeationincreases, and at sufficiently high shear rates the oil droplet breaks up intotwo segments. The results of numerical simulations indicate that dropletbreakup at the pore entrance is facilitated at lower surface tension, higheroil-to-water viscosity ratio and larger droplet size but is insensitive to thevalue of the contact angle. Using simple force and torque balance arguments, anestimate for the increase in critical pressure due to crossflow and the breakupcapillary number is obtained and validated for different viscosity ratios,surface tension coefficients, contact angles, and drop-to-pore size ratios.
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