Small frictional differences yield motion in opposing directions: separation of dry granular materials via horizontal dual-mode vibrations

Recent work has established that objects placed on a horizontally vibrating surface exhibit net motion in one direction if the vibration has multiple frequency modes that break temporal symmetry. Here we report that granules with small differences in friction coefficient can move in opposite directions in response to specific vibratory waveforms, yielding an extremely rapid separation. We use a shooting method numerical simulation to predict the object’s steady velocity by applying Coulomb’s friction law balanced with inertia. Given the frictional properties of the granular materials, we conduct numerical studies to predict the optimal choice of vibratory waveform that induces maximum and opposite steady velocities. We present experimental tests of separating granular materials, millimeter-scale objects, and agricultural products, and we discuss the implications for efficient separation and purification in various industrial processes.