Francesca Messina

An extended and total flux normalized correlation equation for predicting single-collector efficiency.

In this study a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. The correlation equation does not exploit the additivity approach introduced by Yao et al. (1971), but includes mixed terms that account for the mutual interaction of concomitant transport mechanisms (i.e., advection, gravity and Brownian motion) and of finite size of the particles (steric effect). The correlation equation is based on a combination of Eulerian and Lagrangian simulations performed, under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a cylindrical control volume. The normalization of the deposited flux is performed accounting for all of the particles entering into the control volume through all transport mechanisms (not just the upstream convective flux as conventionally done) to provide efficiency values lower than one over a wide range of parameters. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation, valid both for point and finite-size particles, is extended to include porosity dependency and it is compared with previous models. Reduced forms are proposed by elimination of the less relevant terms.

On the failure of upscaling the single‐collector efficiency to the transport of colloids in an array of collectors

Defining the removal efficiency of a filter is a key aspect for colloid transport in porous media. Several efforts were devoted to derive accurate correlations for the single-collector removal efficiency, but its upscaling to the entire porous medium is still a challenging topic. A common approach involves the assumption of deposition being independent of the history of transport, that is, the collector efficiency is uniform along the porous medium. However, this approach was shown inadequate under unfavorable deposition conditions. In this work, the authors demonstrate that it is not adequate even in the simplest case of favorable deposition. Computational Fluid Dynamics (CFD) simulations were run in a vertical array of 50 identical spherical collectors. Particle transport was numerically solved by analyzing a broad range of parameters. The results evidenced that when particle deposition is not controlled by Brownian diffusion, nonexponential concentration profiles are retrieved, in contrast with the assumption of uniform efficiency. If sedimentation and interception dominate, the efficiency of the first sphere is significantly higher compared to the others, and then declines along the array down to an asymptotic value. Finally, a correlation for the upscaled removal efficiency of the entire array was derived