Non-equilibrium thermodynamics beyond linearity: sliding friction

Abstract

Nevertheless, sliding friction is frequent and it was the first irreversible process we were faced in the school, very rare effort has been aimed to develop its non-equilibrium thermodynamic theory if ever. The reason may be guessed as Coulomb’s (Amonton’s 3rd) law is often taught as if it were the final solution, even the velocity dependence of the friction force is rarely mentioned in textbooks or in papers, looking away from its direction. On the other hand, the phenomenon can not be accounted with a linear theory even in the Onsagerian sense. Coulomb’s law displays a strong singularity at equilibrium, which is, at least, extremely rare in nature. On the ground of the thermodynamic theory of rheology, one can guess, that the singularity is virtual. The friction force do depend on the magnitude of the velocity and the function is continuous but it starts so steeply and falls back at practically very low values that to observe it is really difficult. If the two solids are separated with a thin layer of a non-Newtonian fluid the thermodynamic theory of the latter can be applied. This is not a nonsense; the independence of the friction force on the contact area is explained—by rather widely accepted ideas—with plastic flow of the materials at the surface region. In the last decades the interest has increased and several theories was published and experimentally verified that explain friction and wear at different circumstances and the results are not like to each other nor to Coulomb’s law. Applying Onsager’s thermodynamics beyond the realm of linearity is more or less like guessing. Not a free brain storm, but severely limited by observations. Here a germ of a thermodynamic theory is sketched without acquiring generality and restricted to stationary sliding. Here the most simple model is looked for to eliminate the gap between static and kinetic friction. It is not a complete idea at all—the transients have been put aside—but may be a guideline for further modeling. The fork the train of thoughts stops at gives way to several kind of possibilities, a number of which—by the authors opinion—may have their own realm of application. Finally, an accurately accountable model is given that may be assumed friction if we pretend not knowing its origin and the law differs significantly from the nearly exclusively used Coulomb’s law. This example supports the idea that friction can not be described in a simple and uniform theory.