(98az) Numerical Simulation of Concentrated Emulsion Flow Through a Pore in Oil/Water Separation

1. Introduction

              A large amount of liquid waste, including oil-in-water (W/O) and water -in- oil (O/W) emulsions, are generated in chemical, metallurgical and food industries. Various technologies such as static separation, centrifuge demulsification, chemical demulsification, and freeze/thaw demulsification have been developed to separate disperse phase from continuous phase. Basically, these technologies make disperse phase much bigger. However, these technologies have disadvantages such as long operation time, big footprint, high cost and low efficiency. Membrane separation process attracts the attention due to the advantages of short operation time, small footprint, low cost and higher efficiency. The porous membranes act as a wetting and a coalescing medium. If feedwater is O/W emulsion, oil droplets attach on the pore walls and then coalesce in the pores. Consequently, oil droplets in permeate side become much bigger than those in feed side and oil phase is then easily separated from water phase by buoyancy force.

              To improve the demulsification efficiency, a number of experimental studies have been performed using various kinds of porous membranes. They investigated the effects of the size of droplet, pore size and surface hydrophilicity of membrane^[1-3]. However, the mechanism of membrane oil-water separation process is still not well understood and such influence factors have not been optimized completely. Though it is important for the clarification of the mechanism and optimization of parameters to understand concentrated droplet motion within the pore, it is difficult to experimentally observe fluid and droplet motion within the pore. In addition, it is also difficult to evaluate the effects of various parameters independently, because current porous membranes are usually prepared by phase separation methods. The phase separation methods can not control the membrane properties such as pore size, tortuosity, porosity and hydrophilicity, independently.

              Numerical simulation is very useful to investigate the fluid and droplet motion within the membrane pores. In the numerical simulation, motions of oil droplets and fluid within the pore can be easily observed and various parameters can be independently evaluated. Darvishzadeh et al investigated the effect of the crossflow velocity and transmembrane pressure on the motion of a single droplet by numerical simulation ^[4]. However, they did not study the demulsification efficiency and dealt only with a single droplet, not dispersed droplets. To our knowledge, there have been no investigations about membrane demulsification by numerical simulation.

              The aim of this study was to newly develop the numerical simulation model to investigate the behavior of concentrated O/W emulsion through a pore, and to clarify the effects of wettability of the pore walls, filtration flux and pore size on the motion of oil droplets and the demulsification efficiency by the developed simulation model.

2. Numerical method

              In this study, we dealt with the large deformation of the oil-water interface, including coalescence and break up of dispersed droplets. In addition, it is necessary to estimate the volume of the droplet in permeate side to evaluate the demulsification efficiency. We used the coupled level set and volume of fluid (CLSVOF) method ^[5] for capturing the interface motion. CLSVOF method can satisfy volume conservation and evaluate the interfacial tension accurately. The VOF method can treat large deformation of the interface accurately and satisfies volume conservation, while this method cannot evaluate the interfacial tension. By contrast, the level set method can calculate the interfacial tension accurately, while this method cannot satisfy volume conservation. CLSVOF method consists of only advantages of both methods.

              The governing equations of fluid flow are the equation of continuity and the Navier-Stokes equation. A Cartesian grid system was used for arrangement of the Eulerian variables. We used a fractional step method to solve the governing equations. Navier-Stokes equations was splitted into four terms consists of the convection term, the diffusive term, the surface tension force term and the pressure gradient term. The convection term was solved by the cubic interpolated pseudo-particle (CIP) method. The central finite difference was applied for diffusive term. The continuum surface tension force (CSF) model developed by Brackbill et al ^[6] was adopted to evaluate the normal component of the surface tension force. The projection method was applied for calculating the pressure gradient term. To impose the contact angle on the membrane surface, we used a method developed by Sussman ^[7]. The interface described by VOF function is extrapolated into the membrane wall as the specified contact angle is satisfied.

              The size of the computational domain was L_x=50 μm, L_y=10 μm. The numbers of the main mesh were 502×102. A membrane with a straight pore was mounted in the computational domain. The membrane thickness and the diameter of a oil droplet set at 10 μm and 3.0 μm, respectively. N-dodecane was used as the dispersed oil phase. O/W emulsion with 51% of volume fraction, flowed into the left boundary and exited from right boundary. For boundary conditions, the inlet velocity on the feed side was constant and uniform. A non-slip boundary condition at walls of membrane was presented. The periodic boundary condition was applied for the upper and lower boundaries. In this study, the effects of the static contact angle walls of the membrane, the filtration flux and the pore size were investigated.

3. Results and discussion

              To investigate the effect of wettability of membrane surface on the motions of oil droplets in a pore, the static contact angle between oil phase and membrane surface was changed in three steps; 45° , 90° and 135° and the filtration flux and the pore size were set at 1.0 m/s and 4.0 μm, respectively. In the case of 45° of static contact angle, oil droplets attach on the wall of a pore and the oil droplets move on a pore surface with wetting. After that, the droplet then stays near the membrane surface at the outlet of the pore due to the high wettability and the existence of wakes having low velocities. The droplet which flows from behind then coalesces with that at outlet of the pore one after another. It is found that this effect brings about enhances the coalescence between the droplets. In the case of 90° of static contact angle, oil droplets also attach on the wall of a pore and the oil droplets move on a pore surface with wetting. However, the droplets hardly stay the outlet of the pore because of the lower wettability. Therefore, the coalescence between oil droplets near the exit of the pore rarely occurs and the size of droplets do not increase so much. In the case of 135° of static contact angle, oil droplets hardly attach on the wall of a pore due to the much lower wettability. Consequently, oil droplets exit the pore without coalescence.

              Based on these investigations, we can indicate that the coalescence of oil droplets is significantly affected by static contact angle of membrane surface. We will also discuss about the effects of the filtration flux and the pore size on the motion of oil droplets in a pore in the presentation.

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