Configuration of air filters based on the constructal theory

Filtration is one of the simplest and most effective ways to separate particulate matter from fluid and filters find diverse application. The filter design is a critical aspect because it impacts performance. The constructal theory is about the generation of flow architecture both in engineered and natural flow systems, as evidenced by numerous applications (e.g. Bejan, 2000; Bejan & Lorente 2006). According to constructal law, the system shape and internal flow architecture do not develop by chance, but result from the permanent struggle for better performance and therefore must evolve in time. In this study we apply the constructal law to filter design with a geometry that is optimized for the capture of submicrometre aerosols which are particularly hazardous. Filters operate at low Reynolds numbers. Their principle of operation is this: an air stream containing particles with concentration Cin is forced through a set of collecting elements (e.g. fibres, beds). Particles approaching the collectors are then transferred from the air stream to the collector surface. The global purpose is that particle concentration at the outlet is the smallest possible. This means that the purpose of the flow architecture is to maximize deposition rate and volumetric density. If the collecting elements are very close to each other (e.g., in the small-porosity limit). The corresponding particle transfer density (mel) is (Reis et al., 2006)