Particulate air pollution has an adverse effect on cardiovascular and respiratory health. Air filtration systems are therefore essential in closed indoor environments. While mechanical filtration is described as an efficient technology, particle filters may act as a source of pollution if not correctly installed and frequently maintained. The sandfish lizard, a sand swimmer that spends nearly its whole life in fine desert sand, inspired us to rethink traditional filtering systems due to its unique ability of filtering sand from its nasal cavity. During a slow, prolonged inhalation, strong cross-flow velocities develop in a certain region of the upper respiratory tract; these cross-flows enhance gravitational settling and force inhaled sand grains towards the wall where they adhere to mucus, which covers the walls in this region. During an intense, cough-like exhalation the particles are blasted out. In this work, the sandfish's aerodynamic filtering system was analyzed experimentally and by computational fluid dynamics simulations to study the flow profile and particle trajectories. Based on these findings, we discuss the development of a biomimetic filtering system, which could have the following advantages: due to the absence of a membrane, total pressure losses can be reduced. The mucus-covered surface would be mimicked by a specifically treated surface to trap particulate matter. Also, the device would contain a self-cleaning mechanism that simulates the lizard's exhalation. This biomimetic filtering system would therefore have an enhanced life-time and it would be low-maintenance and therefore economical and sustainable.