An important problem in the theory of lubrication is to model and analyze the effect of surface roughness on, for example, the friction and load carrying capacity. A direct numerical computation is often impossible since an extremely fine mesh is required to resolve the surface roughness. This suggests that one applies some averaging technique. The branch in mathematics which deals with this ty...

This paper describes the modelling and testing of mm-scale hydrodynamic bearings which are being developed to improve the efficiency of a cm-scale turbine energy harvester, whose efficiency was previously limited by poorly lubricated commercial jewel-bearings. The bearings were fabricated using DRIE and their performance was assessed using a custom built MEMS tribometer. Results demonstrate tha...

This paper describes the modelling and testing of mm-scale hydrodynamic bearings which are being developed to improve the efficiency of a cm-scale turbine energy harvester, whose efficiency was previously limited by poorly lubricated commercial jewel-bearings. The bearings were fabricated using DRIE and their performance was assessed using a custom built MEMS tribometer. Results demonstrate tha...

The theory of stick-slip is developed, based on the concept of a static and dynamic coefficient of friction. The dynamic coefficient is assumed to be independent of displacement and to depend wholly on normal stress across the surface. It is also assumed to be velocity-independent. The theory predicts that the stress drop during stick-slip is independent of machine stiffness. The displacement d...

We report a quartz crystal microbalance (QCM) study of sliding friction for solid xenon monolayers at 77 K on Cu(111), Ni(111), graphene/Ni(111), and C(60) substrates. Simulations have predicted a strong dependence of phononic friction coefficient (eta) on surface corrugation in systems with similar lattice spacing, eta approximately U(2)(0), but this has never before been shown experimentally....

This manuscript is a survey on results related to boundary layers and the vanishing viscosity limit for incompressible flow. It is the lecture notes for a 10 hour minicourse given at the Morningside Center, Academia Sinica, Beijing, PRC from 11/28 to 12/07, 2007. The main topics covered are: a derivation of Prandtl’s boundary layer equation; an outline of the rigorous theory of Prandtl’s equati...

We study the non-contact friction between an atomic force microscope tip and a metal substrate in the presence of bias voltage. The friction is due to energy losses in the sample created by the electromagnetic field from the oscillating charges induced on the tip surface by the bias voltage. We show that the friction can be enhanced by many orders of magnitude if the adsorbate layer can support...

This survey is devoted to the significant role of various dry friction laws in engineering sciences. Both advantages and disadvantages of a frictional process are illustrated and discussed, but excluding the nature of friction. It is shown how the classical friction laws and modern friction theories exist in today’s pure and applied sciences. Static and dynamic friction models are described. An...

Expressions for variation of skin friction with Reynolds number in fully developed turbulent channel/pipe flows and in zero pressure gradient boundary layers are derived. The proposed in this paper asymptotic (Reδ = δ(x)U ν → ∞) theory is formulated as a convergent perturbation expansion in powers of small dimensionless parameters dδ dx → 0 and u∗ U → 0 applied directly to the Navier-Stokes equ...

A theory to describe the conversion of poloidal momentum into toroidal momentum by phase space structures in trapped ion resonance driven turbulence is presented. In trapped ion resonance driven turbulence, phase space structures are expected to form and can contribute to transport by exerting dynamical friction. Toroidal momentum flux by dynamical friction is calculated. It is shown that dynam...