A numerical study of the effects of loading from diffusive deposition on the efficiency of fibrous filters

This work is aimed at developing numerical methods for calculating diffusive and interceptive deposition on fibres in fibrous filters as a deposit builds up. Calculations are performed of the two dimensional flow field past a single fibre for three different cell models using the boundary element model (BEM). Boundary conditions for the cells correspond to the Kuwabara model and two different rectangular cases, one corresponding to a periodic cell array. The concentration field for particles is then calculated using the equation of Stechkina and Fuchs (1966), but with the numerical flow field. Resulting deposition rates are compared with their results and also with those of Friedlander (1977) for point particles. For deposition on the front of the fibre, we extend their results using the analytic flow field to obtain analytic results for parameter regions where different types of deposition occur. The two relevant parameters are the ratio of the particle to fibre radii and the effective thickness of the diffusion layer. Numerical flow fields are used to calculate particle deposition over the whole fibre, assuming the deposit forms as a smooth solid layer. The new surface shape is parameterised, and the whole process of recalculating the flow field and particle deposition is repeated. Results are obtained for deposition on the new surface as functions of flow Peclet number and fibre packing fraction.