Abstract
A small object (Solid or droplet) is placed on a horizontally vibrating plate, imposing an acceleration γ(t) in the form of a white noise. The object experiences dry friction (due to soild/solid interaction, or to contact angle hysteresis in the case of a droplet). The object is driven by a force γ(t) – Δσ(t) where σ(t), =±1, depending on the sign of the velocity. We discuss the motion at two levels: (i) in terms of simple scaling laws, (ii) by a propagator technique. (a) When Δ is below a certain crossover value Δ*, we expect an unperturbed (Langevin) Brownian motion. (b) When Δ > Δ*, we expect a reduced diffusion coefficient proportional to Δ−4 for small Δ.
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References
D. Tabor F.P. Bowden (1974) A lucid introduction to the whole field is Friction Heinemann London
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Gennes, P.G.d. Brownian Motion with Dry Friction. J Stat Phys 119, 953–962 (2005). https://doi.org/10.1007/s10955-005-4650-4
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DOI: https://doi.org/10.1007/s10955-005-4650-4