Nanohydrodynamics, Friction Forces and Amontons’ Law:from the molecular to the macroscopic sca

Uzi Landman
Georgia Institute of Technology

Computationally-based theoretical modeling and simulations play an increasingly important role in modern condensed matter physics, chemistry, materials science, and biology. In particular, such studies, that may be called “computational microscopies”, allow explorations of complex phenomena with refined resolution in space and time [1]. The use of atomistic simulations as tools of discovery will be discussed and demonstrated through a discussion of two simulation-based studies:

1. Molecular dynamics simulations of the formation and breakup of liquid jets of nanoscale dimensions, lead to a stochastic formulation of the Navier-Stokes equations, thus extending continuum hydrodynamics to the nanoscale domain. The emergence of new classes of break-up solutions for nano-scale liquid structures, differing from those found for the corresponding macroscopic ones, will be analyzed [2].

2. Amontons’ law, which was already known to Leonardo da Vinci, states that the friction force is directly proportional to the (normal) applied load, with a constant of proportionality - the friction coefficient - that is constant and independent of the contact area, the surface roughness and the sliding velocity. No theory has yet satisfacorily explained this surprisingly general law, all attempts being model or system dependent. On the basis of large-scale molecular dynamics simulations pertaining to lubricated adhesive and non-adhesive junctions, with morphologically rough (as well as crystallographically flat) confining solid surfaces, and in conjunction with recent experiments, we show that the local energy-dissipation mechanisms are not 'mechanical', as assumed in most models, but “thermodynamic” in nature. We show that a local analysis of the simulation results, based on division of the system into small cells, leads to a natural description in terms of the Weibull distribution. For the dynamic. non-equilibrium, energy-dissipating process that we study, this long-tail distribution serves a similar purpose as the Boltzmann distribution for classical systems at equilibrium. While Amontons law does not hold on the local scale, it is recovered on the global scale, with the spatio-temporal averaging utilizing the Weibull distribtion of the local friction forces. Interestingly, the concept of "area of contact", often used in frictional studies, does not enter into our analysis [3].

1. U. Landman, “Materials by Numbers: Computations as Tools of Discovery”, Perspective article in Proc. Nat. Acad. Sci. (USA) 102, 6671 (2005).

2. (a) M. Moseler and U. Landman, Science, 289, 1165 (2000); (b) W. Kang and U. Landman, to be published.

3. J. Gao, W. D. Luedtke and U. Landman, Feature article in J. Phys. Chem. B 108, 3480 (2004).

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