(398ah) Investigation of Permeation of Dispersed Particles Through a Pore and Transmembrane Pressure Behavior in Dead-End Constant-Flux Microfiltration Using Direct Numerical Simulation

Introduction

Microfiltration (MF) plays an important role in water treatment processes. Constant-flux filtration, by which end users can obtain a constant desired supply of filtered water, is often used in water treatment processes by MF. In the case of the constant-flux filtration, the transmembrane pressure represents the filtration performance of the MF membrane. It is important in water treatment processes to understand the filtration dynamics of dispersed particles, because these govern transmembrane pressure behavior  corresponding directly to the pumping power required to supply the feedwater. During dead-end MF, particles could permeate the pores in some cases where the particle size is smaller than the membrane pore size. It is well-known that the transmembrane pressure increases due to the membrane fouling. However, it is not as well understood that the transmembrane pressure also increases by the hydrodynamic interactions between fluid and particles, without fouling, as the suspension permeates through the membrane. This is because it is very difficult to experimentally study the flow characteristics and particle motions within the pore that influence hydrodynamic interactions. The aim of this study was to investigate the effects of fluid and particle motions on transmembrane pressure behavior during dead-end, constant-flux filtration. The effects of pore size on the transmembrane pressure were investigated under constant-flux microfiltration. On the basis of these investigations, we clarify the effect of hydrodynamic interactions between the fluid and particles on the transmembrane pressure.

Numerical method

The governing equations of fluid flow are the equation of continuity and the Navier-Stokes equation. The interaction force between the particle and fluid is described as the momentum exchange at the fluid-particle interface. The momentum exchange is solved by the immersed boundary method developed by Kajishima et al[1] without specification of the boundary condition around the particles. The motion of each particle was tracked with a Lagrange scheme by solving the equations of linear momentum and angular momentum. Hydrodynamic, electrostatic, van der Waals, and contact forces are considered as forces acting on a particle.

The computational domain is assumed for the simulation of dead-end, constant-flux filtration. The size of the domain was L_x = 20.0d, L_y = 6.0d and L_z= 6.0d, where d is the diameter of 1.0 μm particles. A membrane with a column straight pore was mounted in the center of the streamwise direction of the computational domain, with the membrane thickness set at 10 μm. The centers of particles were initially placed at x = 1.0 μm and then flowed in with the same translational velocity as the inlet uniform velocity of the fluid. To investigate the effect of pore size on the transmembrane pressure, the pore diameter D was changed in three steps of 2.0, 3.0, and 5.0 μm.

Results and Discussion

In all cases, particles move with the fluid flow and the fluid velocity around the particles then decreases when particles enter the pore. On the other hand, the central velocities in all cases do not decrease significantly as particles penetrate and pass through the pore. This results indicates that the effects of particle penetration on hydrodynamic resistance do not differ significantly with pore size. We investigated the time variations of normalized transmembrane pressure, Δp/Δp₀. Δp is normalized by the transmembrane pressure at steady state without particles. The calculated result revealed that, the mean values of Δp/Δp₀were similar in all cases. In addition, the number of particles that permeate per unit time are also similar in all cases because the volume fractions of feedwater and the water flux rate are the same in the present conditions. These tendencies are consistent with the velocity field as described above. On the other hand, the transmembrane pressure behaviors show periodicity in all cases. The peaks correspond to the times when particles are positioned at the inlet and outlet of the pore. Particles constantly enter from the inlet of the computational domain in the present conditions, giving rise to the transmembrane pressure periodicity. The peak values in the case of D = 2.0 μm are much higher than those in other cases because the velocity gradient at the inlet and outlet of the pore becomes sharp with decreasing pore size. This sharp velocity gradient contributes a high drag force between the fluid and particles.

Reference

[1]Kajishima, T. et al., Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding. JSME Int. J., Ser, B 2001, 44, 526