Particle filtration: A comparison between theory and experiment

The process of filtration of non-charged, submicron particles represents an example of transport in homogeneous and heterogeneous porous media that can be analyzed using the method of volume averaging. In this article the authors develop the local volume averaged particle transport equation for a homogeneous filter and compare the results with experimental data. The particle continuity equation is represented in terms of the first correction to the Smoluchowski equation that takes into account particle inertia effects for small Stokes numbers. This leads to a cellular efficiency that contains a minimum in the efficiency as a function of the particle size, and this allows them to identify the most penetrating particle size. Comparison of the theory with experimental results indicates that the first correction to the Smoluchowski equation gives reasonable results for the most penetrating particle size and for smaller particles; however, results for larger particles clearly indicate the need to extend the Smoluchowski equation to include higher order corrections. The influence of local heterogeneities on the measured filter efficiency may account for some of the observed differences between theory and experiment