Oil droplet behavior at a pore entrance in the presence of crossflow: Implications for microfiltration of oil–water dispersions

Abstract

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 critical pressure for microfiltration of oil-in-water emulsions using slotted-pore membranes

“…1. The numerical methodology for the problem of an oil droplet at a slotted pore is very similar to the numerical setup used in our previous papers, where the permeation, rejection and breakup of an oil droplet at a circular pore was investigated for a number of material parameters and various operating conditions [17,18]. In particular, we performed test simulations to determine the appropriate domain size and grid resolution necessary to accurately capture the effects of interface curvature and flow around the droplet.…”

“…As an aside, an analytical expression for the critical permeation pressure in the case of a continuous oil film above a membrane surface with a pore of arbitrary crosssection was obtained and validated for rectangular and elliptical pores [17]. It was later shown that in the presence of crossflow along the membrane surface, the critical pressure increases due to the drag force generated by the shear flow around an oil droplet, and, at sufficiently high shear rates, the droplet above the pore breaks up into two segments [17][18][19]. The results of numerical simulations have demonstrated that the breakup capillary number and the increase in critical pressure due to crossflow are nearly independent of the contact angle but depend strongly on the oil-to-water viscosity ratio, surface tension, and drop-to-pore size ratio [18].…”

“…It was later shown that in the presence of crossflow along the membrane surface, the critical pressure increases due to the drag force generated by the shear flow around an oil droplet, and, at sufficiently high shear rates, the droplet above the pore breaks up into two segments [17][18][19]. The results of numerical simulations have demonstrated that the breakup capillary number and the increase in critical pressure due to crossflow are nearly independent of the contact angle but depend strongly on the oil-to-water viscosity ratio, surface tension, and drop-to-pore size ratio [18]. Recent experimental studies on crossflow microfiltration have shown that membrane fouling might involve several stages, namely, droplet attachment and clustering, droplet deformation and coalescence [20] and that the critical flux decreases with salt concentration [21].…”

A multicontinuum approach for the problem of filtration of oily‐water systems across thin flat membranes: II. Validation and examples

“…The generated shear stresses at the membrane surface, due to the crossflow velocity, CFV, tend to sweep off accumulated oil droplets. Several modeling approaches have been proposed to investigate the permeation mechanisms across the membrane . More details about these models can be found in the first part of this work .…”

“…They may, generally, be categorized into three approaches according to the level of details they produce. From models that generate integrated details about the filtration processes (e.g., Hermia models and Ho and Zydney model) to models which require comprehensive level of details like those involving computational fluid dynamics (CFD) . In our previous work, a new methodology has been introduced that not only estimates the permeation flux of the water but also the associated oil phase.…”