Stochastic theory of ultrathin lubricant film melting in the stick-slip regime

Abstract

-Melting of an ultrathin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of selforganized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process.

Thermodynamic Theory of Two Rough Surfaces Friction in the Boundary Lubrication Mode

“…11 we obtain h i in different moments of time, and time dependencies of main quantities (F (t), V (t), etc.) have stochastic components [34]. Fig.…”

“…In this figure it is visible that the both quantities are changed during time, and velocity V has a stochastic component [34,35]. But in [34,35] in order to take into account random effects the stochastic terms were introduced into the basic equations. In the present work the stochastic behavior is the result of roughness of rubbing surfaces.…”

Temperature dependence effect of viscosity on ultrathin lubricant film melting

“…Let us use the power dependence for the approximation of η(T ) (6). In that case in the initial system (2)- (4) the second equation assumes the form…”

“…In works [4][5][6][7][8][9][10]] the boundary friction is described which is realized in the case of ultrathin films with thickness less than four diameters of molecules, at smooth or rough surfaces, high loads and small shear rates. It is known that shear viscosity of lubricant layer depends on a temperature [11][12][13][14].…”

“…Thus, at the derivation of basic equations describing the process of friction, it is necessary to define the explicit form of temperature dependence of viscosity. In the previous works [4][5][6][7][8][9][10] the simplest dependence of viscosity on temperature was used. However, actually, it takes different forms for specific systems.…”