A new periodic cell model of aerosol diffusion deposition in a fibrous filter

Abstract

A new periodic cell model for the convective-diffusive transport of small aerosol particles in a fibrous filter is developed. The proposed periodic model takes into account the influence of the fiber diffusion wake on the particle deposition. This allows us to predict the efficiency of a filter more accurately compared to the single-fiber approximations. The fluid flow is described in the framework of Stokes flow in a rectangular periodic cell. New form of periodic boundary conditions for the particle transport equation in the cell is suggested. The equations of fluid flow and particle transport are solved using the Boundary Element Method (BEM) and Boundary Domain Integral Method (BDIM). The diffusive deposition of nanoaerosols in the filter, modeled as a row of the large number of circular cylinders located perpendicular to the flow direction, is studied numerically using the many fibers model. It is shown, that predictions of the new periodic model are in the better agreement with the many fibers model for the filters of greater length. It is also shown, that the widely used approximation for single fiber deposition efficiency (Stechkina, 1967) overestimates the efficiency of multi-fiber filter compared to periodic model. The overestimation increases with increase of Peclet number. The approximate formula for the single fiber particle deposition efficiency in a periodic cell for a square and staggered cylinder arrays is derived. The formula accounts for the effect of the Peclet number and the hydrodynamic factor. The predictions of the derived formula are compared to the numerical data from the work of Hosseini and Tafreshi (2010) for the fibrous filter comprised of many randomly arranged cylinders. The predictions of the diffusive deposition efficiency obtained using the derived formula for the staggered fibers array are shown to be in a good agreement with the numerical model predictions.