Particle filtration: An analysis using the method of volume averaging

The process of filtration of non-charged, submicron particles is analyzed using the method of volume averaging. 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 us to identify the most penetrating particle size. Comparison of the theory with results from Brownian dynamics indicates that the first correction to the Smoluchowski equation gives reasonable results in terms of both the cellular efficiency and the most penetrating particle size. However, the results for larger particles clearly indicate the need to extend the Smoluchowski equation to include higher order corrections. Comparison of the theory with laboratory experiments, in the absence of adjustable parameters, provides interesting agreement for particle diameters that are equal to or less than the diameter of the most penetrating particle