Air-induced inverse Chladni patterns

H.J. van Gerner, J.P. van der Weele, Martin Anton van der Hoef, Roger M. van der Meer

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When very light particles are sprinkled on a resonating horizontal plate, inverse Chladni patterns are formed. Instead of going to the nodal lines of the plate, where they would form a standard Chladni pattern, the particles are dragged to the antinodes by the air currents induced by the vibration of the plate. Here we present a detailed picture of the mechanism using numerical simulations involving both the particles and the air. Surprisingly, the time-averaged Eulerian velocity, commonly used in these type of problems, does not explain the motion of the particles: it even has the opposite direction, towards the nodal lines. The key to the inverse Chladni patterning is found in the averaged velocity of a tracer particle moving along with the air: this Lagrangian velocity, averaged over a vibration cycle, is directed toward the antinodes. The Chladni plate thus provides a unique example of a system in which the Eulerian and Lagrangian velocities point in opposite directions
Original languageUndefined
Pages (from-to)203-220
Number of pages18
JournalJournal of fluid mechanics
Publication statusPublished - 2011


  • METIS-284023
  • particle/fluid flow
  • Granular media
  • IR-79564

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