A Correlation for the Collector Efficiency of Brownian Particles in Clean-Bed Filtration in Sphere Packings by a Lattice-Boltzmann Method

Abstract

In this paper, we develop a new correlation for the clean-bed filter coefficient (lambda0) for Brownian particles, for which diffusion is the main deposition mechanism. The correlation is based on numerical Lattice-Boltzmann (LB) simulations in random packings of spheres of uniform diameter. We use LB methods to solve the Navier-Stokes equation for flow and then the advection-diffusion equation for particle transport. We determine a correlation for an "equivalent" single-collector diffusion efficiency, etaD, so that we can compare our predictions to "true" single-collector correlations stemming from unit-cell modeling approaches. We compared our new correlation to experiments on the filtration of latex particles. For small particle diameters, 50 nm < dp < 300 nm, when gravity and interception are negligible, our correlation for etaD predicts measurements better than unit-cell correlations, which overestimate etaD. The good agreement suggests that the representation of three-dimensional transport pathways in porous media plays an important role when modeling transport and deposition of Brownian particles. To model larger particles, for which gravity and interception are important too, we build a correlation for the overall single-collector efficiency eta0 by adding corresponding etaG and nI terms from unit-cell correlations to our etaD model. The resulting correlation predicts experiments with latex particles of dp > 300 nm well.

Aggregation of silica nanoparticles and its impact on particle mobility under high-salinity conditions

“…Fig. 8 shows the adsorbed mass of nanoparticles decreased with an increase of aggregate sizes consistent with the simulation results by other researchers (Long and Hilpert, 2009;Ma et al, 2009;Nelson and Ginn, 2011;Tufenkji and Elimelech, 2004;Yao et al, 1971) that the deposition of particles would decrease as particles grow in size up to $ 1000 nm due to the reduced Brownian motion. It is anticipated that the size-dependent deposition trend is valid with surface-treated silica aggregates in the size range tested here.…”

Dynamics of particle loading in deep-bed filter. Transport, deposition and reentrainment

“…It can be a very useful tool for designing filter structures which optimize maximum filter lifetime with the acceptable values of filtration efficiency and pressure drop. By using the Lagrangian approach of Brownian dynamics, the model avoids the problem of numerical instability, which was reported by Long and Hilpert (2009) …”

“…Some papers (Dunnett and Clement, 2006;Dunnett and Clement, 2012) take into account deposit growth, but the approach requires making assumptions of deposit structure. The important advantage in deep bed filtration modeling was introduction of lattice gas automata (Biggs et al, 2003) and lattice-Boltzmann method (Long and Hilpert, 2009), that allows to take into account the geometry of flow change due to deposition of suspended particles. Biggs et al (2003) have studied the deposition of particles in 2D constriction unit cell and random 2D porous medium.…”

“…Biggs et al (2003) have studied the deposition of particles in 2D constriction unit cell and random 2D porous medium. Long and Hilpert (2009) have studied the filtration in sphere packings, using advectiondiffusion equation for transport of particles. By performing the set of numerical experiments the authors have developed the correlation for diffusional efficiency, but interception and sedimentation efficiency could be only obtained by employing terms from unit cell correlations.…”

Diesel particulate filter design simulation: A review

“…Narsilio et al 34 applied a finite element method solver COMSOL to calculate the soil hydraulic conductivity. Long and colleagues 35,36 studied the collection efficiency in clean-bed filtration in sphere collectors by lattice Boltzmann method (LBM). Boccardo et al 37 also studied the collection efficiency of various geometries, in which fluid flow was solved by finite volume method and the particle was simulated in a Eulerian way.…”