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

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...

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Published inPhysical review research Vol. 7; no. 3; p. L032001
Main Authors Abramian, Anaïs, Protière, Suzie, Lazarus, Arnaud, Devauchelle, Olivier
Format Journal Article
LanguageEnglish
Published American Physical Society 01.07.2025
Subjects
Condensed Matter
Mechanics
Physics
Statistical Mechanics
Vibrations
random walk
diffusion
Chladni figures
Online AccessGet full text
ISSN2643-1564
2643-1564
DOI10.1103/PhysRevResearch.7.L032001

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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.
AbstractList 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.
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. Published by the American Physical Society 2025
ArticleNumber L032001
Author Lazarus, Arnaud
Abramian, Anaïs
Protière, Suzie
Devauchelle, Olivier
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Snippet 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...
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....
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SubjectTerms Condensed Matter
Mechanics
Physics
Statistical Mechanics
Vibrations
Title Chladni patterns explained by the space-dependent diffusion of bouncing grains
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