Gas-Enabled Resonance and Rectified Motion of a Piston in a Vibrated Housing Filled With a Viscous Liquid

We show how introducing a small amount of gas can completely change the motion of a solid object in a viscous liquid during vibration. We analyze an idealized system exhibiting this behavior: a piston in a liquid-filled housing with narrow gaps between piston and housing surfaces that depend on the piston position. Recent experiments have shown that vibration causes some gas to move below the piston and the piston to subsequently move downward against its supporting spring. We analyze the analogous but simpler situation in which the gas regions are replaced by bellows with similar pressure–volume relationships. We show that the spring formed by these bellows (analogous to the pneumatic spring formed by the gas regions) enables the piston and the liquid to oscillate in a mode with low damping and a strong resonance. We further show that, near this resonance, the dependence of the gap geometry on the piston position produces a large rectified (net) force on the piston. This force can be much larger than the piston weight and tends to move the piston in the direction that decreases the flow resistance of the gap geometry.