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 then considered as parallel connection of unit cells with the cylindrical collector 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 analytical solution of the Stokes problem of transverse flow past the row of equal, 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 it is limited to the viscous regime (fluid inertia negligible) which is typically obeyed for air filtration in fibrous filters. Unit cell deposition efficiency for deterministic mechanisms (i.e., inertial impaction, sedimentation, electrostatic attraction) was calculated by integration of particles equation of motion and then by iterative searching for the limiting trajectories. For the stochastic mechanism of Brownian diffusion a semi-empirical dimensionless correlation was used to compute a single cell deposition efficiency. The combined efficiency of elementary layer due to both - deterministic and stochastic - kinds of mechanisms was calculated assuming that they operate independently. Additionally, the deposition efficiency was corrected by the particle adhesion probability term being dependent on the particle kinetic energy at the moment of collision with a collector. Finally, the total filter efficiency of the multilayer structure was determined numerically as a function of various process parameters.