Intermediate Friction Research Articles

Coupling of translational and reactive dynamics for a Fokker–Planck model

The coupling of translational and reactive dynamics is investigated for a Fokker–Planck description of relative particle motion in a solvent. A division into inner and outer relative coordinate spatial regions separated by a boundary layer is made. The inner region is characterized by a deep potential well associated with bound, or reacted, particles and a potential barrier. The outer zone is characterized by less rapidly varying forces which include solvent structural effects. With this division, a Fokker–Planck source equation for unreacted particles is derived. The source in this equation incorporates the complete inner region dynamics involving both reactive and nonreactive trajectories. This equation is then reduced via projection operator techniques to a spatial Smoluchowski source equation for unreacted particles in the outer region for the case of slow reaction. Validity conditions involving velocity relaxation are given. The sources here include both inner region short range repulsive effects and a reversible chemical reaction. The outer Smoluchowski description includes caging effects. The equivalent boundary condition formulation is given; thus, the radiative boundary condition relating diffusive and reactive fluxes is derived. New expressions for the reaction rate constants are found and examined in terms of more fundamental rate kernels and Fokker–Planck barrier crossing dynamics. The rate constants are evaluated for a Kramers-type treatment of the inner region. These rate constants include effects of velocity nonequilibrium. They reduce to transition state results under intermediate inner region friction conditions.

On the calculations of the diffusion coefficients of oxygen and nitrogen in niobium

The Snoek peaks for oxygen and nitrogen in niobium have been remeasured using a torsion pendulum equipped with LVDT transducers connected to an oscillograph for automatic data recording. The peak temperatures were determined using a new numerical analysis of the peak shape. These new low temperature data have been combined with high temperature direct data and intermediate temperature high frequency internal friction data reported in the literature. When it is assumed that the oxygen and nitrogen] occupied octahedral positions in the niobium matrix, the diffusion coefficients for both oxygen and nitrogen atoms follow a simple Arrhenius behavior. In the temperature range of this analysis (140 to 1000°C for oxygen and 270 to 1800°C for nitrogen) the equationsD = (5.3E - 7) exp - (1.095E5)/RT andD = (2.6E - 6) exp - (1.523E5)/RT apply for the diffusion of oxygen and nitrogen, respectively. Entropy of activation calculations were made using the above activation energies and frequency factors, and the results agree well with reported values for other systems as well as with the theory of Keyes. This good agreement suggests that the assumption that oxygen and nitrogen prefer octahedral sites is probably correct.

Resonant oscillations in closed tubes: the solution of Chester's equation

A closed tube is considered in which the oscillations of a gas column are driven by the sinusoidal motion of a piston. The case where the frequency of the gas column in the tube lies near one of its resonant frequencies is of special interest. The aim of this paper is to extend the theory of Chester (1964), who has given solutions in the inviscid case and for very small boundary-layer friction, to cases of frictional effects of arbitrary strength. This is done by means of a combination of analytical and numerical methods. Different methods are applied for different strengths of the boundary-layer friction. The cases where the influence of the Stokes boundary layer is either very strong or very weak are not especially difficult to treat. The main part of this paper considers cases of intermediate friction, i.e. when the shock strength has grown rather small owing to the influence of the Stokes boundary layer. To obtain an overall view of the phenomena which occur in the Merent regions, a number of solutions have been calculated.

Seismic Response of Pipelines on Friction Supports

The nonlinear responses of two pipeline configurations, which are representative of an aboveground crude oil pipeline, are studied. Resistance to horizontal movement is provided by a combination of widely spaced anchor supports and intermediate friction supports. Following the application of operating pressure and thermal loads, the systems are subjected to strong earthquake ground motions. Results show that the inertia forces that develop during an earthquake tend to negate the restraining effect of the friction forces in the operating condition. This causes the pipe to move toward the position it would assume if there were no friction. The earthquake motion may result in either an increase or decrease in the critical bending moment depending on the geometrical configuration and the earthquake acceleration level.

Establishing a rule for the tyre load variations in respect to speed. (in Italian) : L. Amici and E. Robecchi, Ricerca e sviluppo, No. 12, November 1959 (Pirelli)

In the present work, the tribological mechanism of diamond-like carbon (DLC) films was investigated. DLC films were coated on metallic substrates (M50 steel, Ti-6Al-4V alloy and AISI 440C steel) by methane ion-beam deposition. Pin-on-disc experiments showed that the DLC films possess excellent wear resistance and exhibit low values of friction coefficient (ƒ < 0.1). The frictional response was characterized by an initial break-in period that was followed by an intermediate constant ƒ stage. The presence of a carbon transfer layer was observed on the wear scars of ball surfaces. Transmission electron microscopy and electron diffraction from the transfer layer showed that it contained a fine distribution of graphite nanoparticles (less than 5 nm) in a distorted diamond-like structure. Laser Raman spectra taken from the wear track region also revealed evidence of graphitization. In light of the present observations, the intermediate friction stage was mainly attributed to transfer layer formation. During long-duration wear experiments, a further reduction in ƒ was observed that finally reached steady state low friction (ƒ = 0.05–0.07) and an ultralow wear rate (about 1.6 × 10−9mm3 m−1 N−1). Steady state was related to the complete transformation of diamond-like to graphite-like carbon under thermal and strain effects from the repeated friction through a precursor stage involving hydrogen evolution and sp3 structure destabilization. The ultra-low wear rates were correlated to easy shear of low-strength atomic carbon interlayers in the graphitic structure.