Simplified Formula for the Critical Entry Pressure and a Comprehensive Insight into the Critical Velocity of Dislodgment of a Droplet in Crossflow Filtration

On the estimation of the size of a droplet emerging from a pore opening into a crossflow field

The problem of terminating a droplet at the surface of a membrane in a crossflow field is an important topic in the context of controlled emulsification of fluids for use in pharmaceutical and other industries. Some of these industries struggle to produce emulsions of uniform sizes for their products requiring higher levels of precision. In this work, we comprehensively investigated one such technique in which droplets were produced via membrane openings and were terminated via a crossflow field. Conditions of permeation and termination were identified. A model was developed to estimate the size of the emerging droplets from information about the interfacial properties, geometry, and operating conditions (i.e., pressure and crossflow velocity). Three forces, including capillary pressure, interfacial tension, and drag forces, were identified that account for a developed torque balance, which was then used to determine the onset of breakup of an emerging droplet. A comprehensive computational fluid dynamics (CFD) analysis has been conducted to highlight the physics involved in the process and also to provide scenarios for comparison exercises. The effects of crossflow velocity, applied pressure, and viscosity contrasts have been studied. It has been determined that the emerging droplet experiences deformation along the crossflow field because of the hydrodynamic drag. The receding portion of the contact line at the surface of the membrane wraps around the pore opening, generating an interfacial tension force that produces an opposing torque due to the crossflow drag and capillary pressure. Using this phenomenon, a framework for estimating the size of the droplet upon breakup is established. Comparisons with the results obtained from the CFD analysis under different conditions show very good agreement, which builds confidence in the modeling approach.

High-Resolution Numerical Simulation of Microfiltration of Oil-in-Water Emulsion Permeating through a Realistic Membrane Microporous Structure Generated by Focused Ion Beam Scanning Electron Microscopy Images

Owing to the limitations of visualization techniques in experimental studies and low-resolution numerical models based on computational fluid dynamics (CFD), the detailed behavior of oil droplets during microfiltration is not well understood. Hence, a high-resolution CFD model based on an in-house direct numerical simulation (DNS) code was constructed in this study to analyze the detailed dynamics of an oil-in-water (O/W) emulsion using a microfiltration membrane. The realistic microporous structure of commercial ceramic microfiltration membranes (mullite and α-alumina membranes) was obtained using an image processing technique based on focused ion beam scanning electron microscopy (FIB-SEM). Numerical simulations of microfiltration of O/W emulsions on the membrane microstructure obtained by FIB-SEM were performed, and the effects of different parameters, including contact angle, transmembrane pressure, and membrane microporous structure, on filtration performance were studied. Droplet deformation had a strong impact on filtration behavior because coalesced droplets with diameters larger than the pore diameter permeated the membrane pores. The permeability, oil hold-up fraction inside the pores, and rejection were considerably influenced by the contact angle, while the transmembrane pressure had a little impact on the permeability and oil hold-up fraction. The membrane structure, especially the pore size distribution, also had a significant effect on the microfiltration behavior and performance.

The Effect of the Oleophobicity Deterioration of a Membrane Surface on Its Rejection Capacity: A Computational Fluid Dynamics Study

In this work, the effects of the deteriorating affinity-related properties of membranes due to leaching and erosion on their rejection capacity were studied via computational fluid dynamics (CFD). The function of affinity-enhancing agents is to modify the wettability state of the surface of a membrane for dispersed droplets. The wettability conditions can be identified by the contact angle a droplet makes with the surface of the membrane upon pinning. For the filtration of fluid emulsions, it is generally required that the surface of the membrane is nonwetting for the dispersed droplets such that the interfaces that are formed at the pore openings provide the membrane with a criterion for the rejection of dispersals. Since materials that make up the membrane do not necessarily possess the required affinity, it is customary to change it by adding affinity-enhancing agents to the base material forming the membrane. The bonding and stability of these materials can be compromised during the lifespan of a membrane due to leaching and erosion (in crossflow filtration), leading to a deterioration of the rejection capacity of the membrane. In order to investigate how a decrease in the contact angle can lead to the permeation of droplets that would otherwise get rejected, a CFD study was conducted. In the CFD study, a droplet was released in a crossflow field that involved a pore opening and the contact angle was considered to decrease with time as a consequence of the leaching of affinity-enhancing agents. The CFD analysis revealed that the decrease in the contact angle resulted in the droplet spreading over the surface more. Furthermore, the interface that was formed at the entrance of the pore opening flattened as the contact angle decreased, leading the interface to advance more inside the pore. The droplet continued to pass over the pore opening until the contact angle reached a certain value, at which point, the droplet became pinned at the pore opening.

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.