Aerosol particle filtration in the fibrous filters at the presence of external electric field. I. Theoretical model

The paper presents theoretical analysis of aerosol particles filtration in a dielectric fibrous filter placed in an external electric field. The real complex geometrical structure of the filter is approximated by a staggered model consisting of sequence of several elementary layers. Each layer is th en considered as parallel connection of unit cells with the cylindrical col lector in the centre. Relative arrangement of the subsequent layers is such that collectors form a hexagonal array, that is the distance from a chosen fibre to each of six closest neighbours is the same. The gas flow pattern in the porous space of the filter was described using an approximate analyt ical solution of the Stokes problem of transverse flow past the row of equa l, parallel circular cylinders (corresponding to the elementary filtrating layer of our geometrical model). Such a method accounts to some extent for the effect of neighbouring fibres on the flow field and pressure drop but i t is limited to the viscous regime (fluid inertia negligible) which is typi cally obeyed for air filtration in fibrous filters. Unit cell deposition ef ficiency for deterministic mechanisms (i.e., inertial impaction, sedimentat ion, electrostatic attraction) was calculated by integration of particles e quation of motion and then by iterative searching for the limiting trajecto ries. For the stochastic mechanism of Brownian diffusion a semi-empirical d imensionless correlation was used to compute a single cell deposition effic iency. The combined efficiency of elementary layer due to both - determinis tic and stochastic - kinds of mechanisms was calculated assuming that they operate independently. Additionally, the deposition efficiency was correcte d by the particle adhesion probability term being dependent on the particle kinetic energy at the moment of collision with a collector. Finally, the t otal filter efficiency of the multilayer structure was determined numerical ly as a function of various process parameters.