Critical role of gravity in filters

The efficiency of filters depends crucially on the mass of the particles one wants to capture. 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 St(c) below which no particles are trapped; i.e., the filter does not work. Above St(c) the capture efficiency increases like the square root of (St-St(c)). 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 penetration profile and as function of the porosity of the filter.