Coalescence of an Oil Droplet with a Permeating One over a Membrane Surface: Conditions of Permeation, Recoil, and Pinning.

When a droplet lands over a nonwetting surface it forms a convex interface that makes a contact angle larger than 90°. If the droplet lands over a pore opening, an interface is also formed at the pore opening that can prevent the droplet from permeating. The conditions for permeation and pinning are very much related to a threshold critical pressure that above which the droplet will permeate. This property defines a selectivity criterion for microfiltration processes of oily water systems using membrane technology. Such a feature of the membrane gets compromised, however, due to the permeation of droplets that are relatively smaller in size or whose critical entry pressure is smaller than the applied transmembrane pressure (TMP). In this work, we investigate what happens to a droplet when it coalesces with a droplet that undergoes permeation. Two scenarios are considered: namely, (1) a droplet coalesces with a permeating one whose interface inside the pore has not broken through the pore exit and (2) a droplet coalesces with a permeating one whose interface in the pore has broken through. We show that a larger droplet (that will essentially not permeate if pinned over a membrane opening) will now permeate when the pore is filled with oil from a preceding one or recoils when the interface inside the pore of a preceding droplet has not broken through the exit of the pore. This has interesting implications for the rejection capacity of the membrane, which decreases due to the permeation of droplets that would, otherwise, not permeate. A computational fluid dynamic (CFD) study has been conducted to confirm the conclusions obtained from the theoretical study and to reproduce the fates of the combined droplet after coalescence at the surface of the membrane. Furthermore, a simplified formula for estimating the critical entry pressure is developed.