Ind. Eng. Chem. Process Des. Dev., Vol. 18, No. 1, 1979
171
A Model of Aerosol Filtration by Fibrous Filters Gordon M. Bragg' and Bruce M. Pearson Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada
An analytic model describing a fibrous filter has been developed. Helical tubes are assumed to represent the flow passages in a filter. The model can be used to predict pressure drop and particle collection efficiency due to inertial impaction and diffusion. The predictions are compared with experiments and appear to be valid for porosities between 0.70 and 0.994 and for fiber diameters greater than 5 pm. The results of the present model are shown to compare quite favorably with those of other models for collection efficiency. Finally, the adaptability of the present model to future improvements is discussed.
Introduction Due to the complicated nature of fluid flow through a fibrous filter, theoretical results for resistance and particle collection efficiency can only be obtained by modeling the actual filter in a c u t a i n manner. The most common modeling technique is to focus on a single fiber in the filter and represent it as an infinitely long circular cylinder, around which the fluid flows. In this type of model, the gas stream flowing through the filter takes the suspended particles close to the cylinder, where a number of short range mechanisms accomplish the actual removal. The basic short range mechanisms are labeled inertial impaction, interception, and Brownian diffusion. Of major importance in analyzing the capture of particles by these mechanisms is the velocity field which surrounds the cylinder. Due to the complexity of solving the Navier-Stokes equations for the exact flow field around a cylinder, many simplifications and approximations have been employed. Kaufmann (1936) used the ideal flow solution for fluid flow around an infinite cylinder to calculate total filter collection efficiency due to the combined effect of inertial impaction, interception, and diffusion. Langmuir (1942) attempted to determine filter collection efficiencies due to interception and diffusion, by using Lamb's viscous flow solution for flow around cylinders. A more in depth discussion of these older models can be found in the work of Davies (1973). Prior to 1959, the most difficult problem in the theory of filtration had been to find a satisfactory expression for the flow around a single cylinder. Expressions for flow around isolated cylinders, such as Lamb's viscous flow solution for low Reynolds numbers, Re, made the resistance to flow a function of the Reynolds number based on fiber diameter. This result was contrary to experience, and it was believed that due to surrounding fibers in a filter, a single fiber could not be considered to be isolated. The other fibers alter the flow field in such a way as to cause the resistance to be independent of Reynolds number. Subsequently, in 1959, Happel (1959) and Kuwabara (19591, independently produced expressions for the flow field around a single fiber which were independent of Reynolds number and depended on the solidity N. Stechkina et al. (1969) have applied Kuwabara's flow field to what they term a fan model to predict fibrous filter efficiency. They claim that their fan model gives accurate results for filters with solidity, O , between 0.0035 and 0.08, and low Reynolds numbers. The fan model consists of rows of parallel cylinders at arbitrary angles between the rows. The approximate, semiempirical solution obtained for the single fiber collection efficiency is given by 0019-7882/79/1118-0171$01.00/0
I = (29.6 2 8 ~ \ ~ ~ ' )-R 27.5R28 * (vi) Here, vu, qR. and '11 are the single fiber collection efficiencies due to diffusion, interception, and inertial impaction, respectively, qDR is the diffusion-interception interference term, Pe is the Peclet number, St is the Stokes number, R is the interception parameter, and K n is the Knudsen number. This solution is valid for Peclet number, P e
