Model of transient aerosol particle deposition in fibrous media with dendritic pattern

When a suspension of fine solid particles in a gaseous medium flows through a fibrous filter, particles deposit on the fibers forming chainlike agglomerates known as dendrites. This deposition pattern is responsible for the intrinsically transient behavior of the filter, leading to drastic increases of the filtration efficiency and of the pressure drop. Related phenomena are observed when aerosols flow through other types of porous media (for example, granular beds), or next to duct walls, around immersed objects, etc. A theoretical model of the particle dendrite growth was proposed recently by Payatakes and Tien. Here a revised and generalized version of that model is developed. The following major revisions are made: allowance is made for collisions with a particle in a given dendrite layer that lead to retension in the same layer, radial as well as angular contributions to deposition are considered, and the dendrite layer adjacent to the collector is allowed to contain more than one particle. These changes lead to a substantially more realistic theoretical model. Expressions for the transient behavior of a filter of differential thickness are obtained, based entirely on first principles. These, as it has been shown in a previous publication, can be used to predict the dynamic behavior of a macroscopic fibrous filter. The use and behavior of this model is demonstrated in the simple case of deposition by pure interception. The present treatment of deposition by pure interception is more rigorous than and supersedes that adopted in previous works.