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
S. Daniel, M. Chaudhury, P.-G. de Gennes, to be published in Langmuir.
A. Buguin, F. Brochard and P.-G. de Gennes, to be published in European Journal of Physics E.
P. Langevin, CR Acad. Sci. (Paris) 530 (1908).
M. von Smoluchowski, work described in Physical Chemistry, S. Berry, S. Rice, J. Ross eds. (Wiley NY, 1980), p. 1164.
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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