a b s t r a c tThis study addresses the issue of oil removal from water using hydrophilic porous membranes. The effective separation of oil-in-water dispersions involves high flux of water through the membrane and, at the same time, high rejection rate of the oil phase. The effects of transmembrane pressure and crossflow velocity on rejection of oil droplets and thin oil films by pores of different cross-section are investigated numerically by solving the Navier-Stokes equation. We found that in the absence of crossflow, the critical transmembrane pressure, which is required for the oil droplet entry into a circular pore of a given surface hydrophilicity, agrees well with analytical predictions based on the Young-Laplace equation. With increasing crossflow velocity, the shape of the oil droplet is strongly deformed near the pore entrance and the critical pressure of permeation increases. We determined numerically the phase diagram for the droplet rejection, permeation, and breakup depending on the transmembrane pressure and shear rate. Finally, an analytical expression for the critical pressure in terms of geometric parameters of the pore cross-section is validated via numerical simulations for a continuous oil film on elliptical and rectangular pores.

The behavior of an oil droplet pinned at the entrance of a micropore and subject to clossflowinduced 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.

The influence of geometrical parameters and fluid properties on the critical pressure of permeation of an oil micro-droplet into a slotted pore is studied numerically by solving the Navier-Stokes equations. We consider a long slotted pore, which is partially blocked by the oil droplet but allows a finite permeate flux. An analytical estimate of the critical permeation pressure is obtained from a force balance model that involves the drag force from the flow around the droplet and surface tension forces as well as the pressure variation inside the pore. It was found that numerical results for the critical pressure as a function of the oil-to-water viscosity ratio, surface tension coefficient, contact angle, and droplet radius agree well with theoretical predictions. Our results show that the critical permeation pressure depends linearly on the surface tension coefficient, while the critical pressure nearly saturates at sufficiently large values of the viscosity ratio or the droplet radius.These findings are important for an optimal design and enhanced performance of microfiltration systems with slotted pores.

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