Bouncing spring

bouncingIn recent years, bouncing droplets have been studied [1,2] in our lab. We have also proposed to model bouncing droplets by bouncing springs [3], elastic deformations are assumed to capture surface tension effects while viscous damping is linked to internal dissipation.

The bouncing spring model has been explored theoretically and numerically. The main results are published in our last article in Physica D [4]. The major features observed for droplets have been reproduced with bouncing springs : bouncing modes, bifurcation diagrams, extreme sensitivity to initial conditions, bouncing thresholds, memory effects, subharmonics, etc…

Asymptotic behaviors are emphasized : the bouncing ball model is recovered for high dissipation and low deformations. We calculate also an analytic expression for the bouncing threshold pointing out resonant effects in such system. This model can be exploited to investigate complex behaviors of bouncing droplets.

[1] S.Dorbolo, D.Terwagne, N.Vandewalle, and T.Gilet, Resonant and rolling droplet, New J. Phys. 10, 113021 (2008)
[2] T.Gilet, D.Terwagne, N.Vandewalle and S.Dorbolo, Dynamics of a bouncing droplet onto a vertically vibrated interface, Phys. Rev. Lett. 100, 167802 (2008)
[3] D.Terwagne, F.Ludewig, N.Vandewalle, S.Dorbolo, The role of the droplet deformations in the bouncing droplet dynamics, Phys. Fluids 25, 122101 (2013)
[4] M.Hubert, F.Ludewig, S.Dorbolo, N.Vandewalle, Bouncing dynamics of a spring, Physica D 272, 1-7 (2014) – PDF

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About nicovdw

Professor in Physics
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