A correlation for the collector efficiency of Brownian particles in clean-bed filtration in sphere packings by a Lattice-Boltzmann method

In this paper, we develop a new correlation for the clean-bed filter coefficient (λ₀) 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, η_D, 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 < d_p < 300 nm, when gravity and interception are negligible, our correlation for η_D predicts measurements better than unit-cell correlations, which overestimate η_D. 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 η₀ by adding corresponding η_G and η_I terms from unit-cell correlations to our η_D model. The resulting correlation predicts experiments with latex particles of d_p > 300 nm well.