Phase-Field Simulation of the Coalescence of Droplets Permeating through a Fibrous Filter Obtained from X-ray Computed Tomography Images: Effect of the Filter Microstructure

Simulation investigation of the spontaneous motion behaviors of underwater oil droplets on a conical surface

A conical surface can realize the spontaneous transportation of micro-sized oil droplets in an aqueous environment without energy input, exhibiting great potential for applications in microfluidics, chemical micro-reactors, water remediation, etc. However, the precise manipulation of an oil droplet on a cone is still very challenging because the dynamic behavior of a droplet on a cone is not fully understood. Herein, the dynamic behavior of oil droplets on a cone is quantitively studied via numerical simulations, and the effects of wettability, apex angle, and droplet size on the droplet's dynamic behavior are systematically analyzed. The results show that the moving velocity and transport distance of the droplet on the cone are highly related to the droplet shape on the cone. It was found that a clamshell-shaped droplet moves faster than a barrel-shaped droplet. Besides, the clamshell-shaped droplet with a larger size, on the cone with a smaller apex angle and smaller contact angle tends to obtain a faster moving speed and a longer transportation distance. The droplet shape adopted on the cone was determined by the cone wettability and the size of the droplet relative to the local curvature of the cone. It was found that the oil droplet tends to form a barrel shape on the cone with a highly oleophilic and small apex angle, and tends to form a clamshell shape on cones with a highly oleophobic and large apex angle. In addition, the droplet might transit from a barrel shape to a clamshell shape when it moves from the cone tip to the cone base, and the trigger time of the transit is negatively correlated with the contact angle and apex angle of the cone. This work provides a microscale understanding of the dynamic behavior of an underwater oil droplet on a cone, and also offers theoretical guidance for manipulating the behavior of a droplet on a cone and for the rational design of cone surfaces for spontaneous droplet transport and droplet collection.

Effect of liquid volume fraction and shear rate on rheological properties and microstructure formation in ternary particle/oil/water dispersion systems under shear flow: two-dimensional direct numerical simulation

We numerically studied the rheological properties and microstructure formation under shear flow in a ternary particle/oil/water dispersion system. Our numerical simulation method was based on a phase-field model for capturing a free interface, the discrete element method for tracking particle motion, the immersed boundary method for calculating fluid-particle interactions, and a wetting model that assigns an order parameter to the solid surface according to the wettability. The effects of the water-phase volume fraction and shear rate on the microstructure and apparent viscosity were investigated. When the water-phase volume fraction was low, a pendular state was formed, and with an increase in the water-phase volume fraction, the state transitioned into a co-continuous state and a Pickering emulsion. This change in the microstructure state is qualitatively consistent with the results of previous experimental studies. In the pendular state, the viscosity increased with an increase in the water-phase volume fraction. This was due to the development of a network structure connected by liquid bridges, and the increase in the coordination number was quantitatively confirmed. In the case of the pendular state, significant shear thinning was observed, but in the case of the Pickering emulsion, no significant shear thinning was observed. It is concluded that this is due to the difference in the manner in which the microstructure changes with the shear rate. This is the first study to numerically demonstrate the microstructure formation of a ternary dispersion under shear flow and its correlation with the apparent viscosity.

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.

Identification of Deposited Oil Structures on Thin Porous Oil Mist Filter Media Applying µ-CT Imaging Technique

The identification of microscale oil structures formed from deposited oil droplets on the filter front face of a coalescence filter medium is essential to understand the initial state of the coalescence filtration process. Using µ-CT imaging and a deep learning tool for segmentation, this work presents a novel approach to visualize and identify deposited oil structures as oil droplets on fibers or oil sails between adjacent fibers of different sizes, shapes and orientations. Furthermore, the local and global porosity, saturation and fiber ratios of different fiber material of the oleophilic filter medium was compared and evaluated. Especially the local and global porosity of the filter material showed great accordance. Local and global saturation as well as the fiber ratios on local and global scale had noticeable differences which can mainly be attributed to the small field of view of the µ-CT scan (350 µm on 250 µm) or the minimal resolution of approximately 1 µm. Finally, fiber diameters of the investigated filter material were analyzed, showing a good agreement with the manufacturer’s specifications. The analytical approach to visualize and analyze the deposited oil structures was the main emphasis of this work.

Simulation Study on the Dynamic Behaviors of Water-in-Oil Emulsified Droplets on Coalescing Fibers

Although increasing superwetting membranes have been developed for separating oil-water emulsions based on the "size-sieving" mechanism, their pores are easily blocked and fouled by the intercepted emulsified droplets, which would result in a severe membrane fouling issue and a sharp decline in flux. Instead of droplet interception, a fiber-based coalescer separates oil/water emulsions by inducing the emulsified droplets to coalesce and transform into layered oil/water mixtures, exhibiting an ability to work continuously for a long time with high throughput, which makes it a promising technology for emulsion treatment. However, the underlying mechanism of the separation process is not well understood, which makes it difficult to further improve the separation performance. Hence, in this work, the dynamic behaviors of water-in-oil emulsified droplets on the surface of the coalescing fiber were numerically investigated based on the phase-field model. The attachment, transport, and detachment behaviors of droplets on fibers were directly observed, and the effects of fiber wettability, orientation, arrangement, and fluid speed were studied in detail. First, it was observed that the droplets will move downstream along the fiber surface under the effect of fluid shear, and the large droplets tend to coalesce with their downstream small droplets on the same fiber surface because they move faster compared to the small droplets. Second, it was found that the emulsified droplet will spontaneously transport to the intersection of two angled fibers under the drive of asymmetric Laplace pressure, which demonstrated that the emulsified droplets tend to gather at the intersection of fibers when permeating through a coalescing medium. Third, it was found that the detachment behaviors of droplets from the fiber surface are strongly affected by their size, fiber wettability, and fluid velocity. In addition, the results of our simulation show that the backside of two closely attached fibers can further inhibit the detachment of droplets. We truly believe that our research results are of significance to optimize the parameters of a fiber-based coalescer for separating oil-water emulsions and to develop novel oil/water separators.