The critical role of gravity in filters

Filters are used in chimneys, water purification, cigarettes and many other everyday situations. The mass of the particles one wants to capture crucially determines the efficiency of the filtering. Using analytical and numerical calculations we reveal a very rich scenario of scaling laws relating this efficiency to particle size and density and the velocity and viscosity of the carrying fluid. These are combined in the dimensionless, so called Stokes number St. In the case of horizontal flow or neutrally buoyant particles we find a critical number Stc below which no particles are trapped, i.e. the filter does not work. Above Stc the capture efficiency increases like the square root of St − Stc. Under the action of gravity, the threshold abruptly vanishes and capture occurs at any Stokes number increasing linearly in St. We discovered further scaling laws in the entire penetration profile and as function of the porosity of the filter.