Inspired by the ability of marine suspension feeders to selectively capture small particles by their hairlike cilia, we simulate the interaction between artificial cilia and microscopic particles of different sizes to determine if a purely synthetic system can display analogous size-selective behavior. Our computational approach specifically models the capture of particles suspended in the surrounding fluid by adhesive filaments, which are anchored by one end to a surface. Via this model, we show that this size selectivity can arise as a result of adhesive and hydrodynamic interactions in the system. The substantial reduction in the mobility of the large particles near surfaces leads to a failure in capturing large particles Using a simple analytical model, we show that the balance of hydrodynamic and adhesive forces favors capture of particles below a critical size for a given cilia-particle interaction. Our findings provide guidelines for designing artificial cilia that can be used for sorting and transporting particles within microfluidic devices.