Effect of air on granular size separation in a vibrated granular bed

Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a nonmonotonic density dependence of the rise and sink time of the large sphere. We show that air drag causes relative motion between the intruder and the bed during the shaking cycle and is ultimately responsible for the observed density dependence of the risetime. We investigate in detail how the motion of the intruder sphere is influenced by size of the background particles, initial vertical position in the bed, ambient pressure, and convection. We explain our results in the framework of a simple model and find quantitative agreement in key aspects with numerical simulations to the model equations.