Constructal theory of particle agglomeration and design of air-cleaning devices

In this paper we propose a constructal approach to understanding and predicting the morphology of agglomerates of aerosol particles and also to the design of air-cleaning devices. We show that particle agglomeration begins in spherical shape and switches to needle-shaped agglomeration, which performs best as a particle collector at long times. The shape of the needle depends on the dipolar moment of the particles, while the critical number of particles prior to switching to needle shape does not depend on the particle properties.We also show how constructal theory leads to the design of air-cleaning devices that achieve maximum performance per unit volume, under the imposed global constrains. The optimal geometry (internal spacing) of devices composed of parallel-plate channels or tubes and porous filters is shown to depend on known non-dimensional numbers that characterize particle deposition. The work reported in this paper adds to many studies that show how constructal theory provides a deterministic basis for the generation of flow configuration everywhere.