Removing dust from confined air volumes - A toy model

Most environments inhabited by living beings have dust. Much of that dust comes from the continuous flaking of our own skin and atmosphere borne particles of submicron size. Dust mites seem to play an important role in integrating fine scale dust, which they consume to grow, resulting in larger length scale dust. Dust continues to agglomerate and grow. Air filters are designed to remove dust and control dust agglomeration. We report a simple scaling law, based on kinematic simulations of dust filtration through a one dimensional idealized filter. The results reveal insights regarding how filters may clog in time. Our results may be of use to someone interested in designing customized air filters for optimum dust removal in an environment with a known dust distribution.