Chladni patterns explained by the space-dependent diffusion of bouncing grains

Abstract

Although Chladni patterns are widely used to visualize the modes of vibration of an elastic plate, the mechanism by which the grains form the pattern is still debated. In this Letter, we suggest that the pattern results from space-dependent diffusion: grains gather where their diffusivity is low. We test this hypothesis in experiments, wherein we generate Chladni patterns on a vibrating membrane. We measure the diffusivity of the grains as a function of the vibration amplitude and propose an expression of the diffusive flux based on our measurements. We find a steady-state distribution of the grains in agreement with observations. These findings could inspire new methods to manipulate and segregate particles.