Lubricating theory

Booser, R. E. (1988). Handbook of Lubrication, Theory and Practice of Tribology Volume II. Boca Raton CRC Press. Bowden, F. P., and Tabor, D. (1964). The Friction and Lubrication of Solids, Parr II Oxford Clarenden Press. Cameron, A. (1996). Principles of Lubrication. New York John Wiley. 

Booser, E. R., (Ed.) Handbook of Lubrication Theory and Practice of Tribology, 1, Application and Maintenance, CRC Press, Boca Raton, USA (1982)... 

Matsuoka, H., andKato, T., "An Ultral-thin Liquid Film Lubrication Theory—Calculation Method of Solvation Pressure and Its Application to the EHL Problem, Trans. ASME, J. Tribol, Vol. 119,1997, pp. 217-226. 

The velocity analysis is of great important for a lubrication theory, which will lay the foundation for further processes, to obtain the flux, the pressure distribution, the load and the friction, etc. As shown before, however, the present model requires a complex procedure to achieve the results. Thus, it can be regarded as a more purely scientihc one," i.e., there is a long way to the success of predictive ability. For a practical purpose, from an engineering point of view, some simplifications should be conducted in an attempt to get the parameters of interest. 

One of the apparent results of introducing couple stress is the size-dependent effect. If the problem scale approaches molecular dimension, this effect is obvious and can be characterized by the characteristic length 1. The size effect is a distinctive property while the film thickness of EHL is down to the nanometre scale, where the exponent index of the film thickness to the velocity does not remain constant, i.e., the film thickness, if plotted as a function of velocity in logarithmic scale, will not follow the straight line proposed by Ham-rock and Dowson. This bridges the gap between the lubrication theory and the experimental results. 

Subsequently, a lubrication theory considering the solvation force is deduced accordingly in such ultra-thin film lubrication. 

Das, N. C., Elastohydrodynamic Lubrication Theory of Line [39] Contacts Couple Stress Fluid Model, Tribal. Trans., Vol. 40, No.2,1997,pp.353-359. 

Historically, gas lubrication theory was developed from the classical liquid lubrication equation—Re5molds equation [4]. The first gas lubrication equation was derived by Harrison [5] in 1913, taking the compressibility of gases into account. Because the classical gas lubrication equation is based on the Navier-Stokes equation, it does not incorporate some gas flow characteristics rooted in the rarefaction effects of dilute gases. As early as 1959, Brunner s experiment [6] showed that the classical gas lubrication equation was... 

The last category is the pressure-driven gas flows, which are typical in micro gas fluidic and micro heat transfer systems. Because the channel diameter or width in micro gas fluidic systems is in the scale of sub-micrometer or less, ultra-thin gas lubrication theory plays an important role in... 

Sundararajan, S. andXhakurta, D., Two-Dimensional Wafer-Scale Chemical-Mechanical Planarization Models Based on Lubrication Theory and Mass Transport, Journal of the Electrochemical Society, Vol. 146, No. 2, 1999, pp. 761-766. 

The second step in Ten Cate s two-step approach was to focus on crystal-crystal interaction by means of an explicit two-phase DNS of the turbulent suspension that completely resolves the translational and rotational motions and collisions of the spherical particles plus the turbulence of the liquid between the particles. The particle motions are driven by the turbulent flow and the particles affect the turbulent flow of the liquid in between. When particles approach one another down to a distance smaller than the grid spacing, lubrication theory is exploited to bridge the gap between them. 

A mathematical analysis of the process is extremely difficult and requires to solve the Reynolds equation of lubrication theory and apply the solution to the cavitation boundary conditions. A two-dimensional analysis of the pressure distribution in the plane of the roll nip showed that the liquid pressure rises sharply to a large value near the nip, and drops equally sharply to a minimum justbeyond the nip. Before large negative pressures are reached, the liquid may cavitate as a result of the expansion of entrained gases within the liquid. 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

Frankel and Acrivos11 have obtained models with well-defined hydrodynamics for very high concentrations of rigid and elastic particles. Here the solvent forms thin films and we enter the region of lubrication theory. The expressions describing the flow do bear some similarities to the semi-empirical expressions developed at lower concentrations. For example Frankel and Acrivos give... 

Szeri, A.Z., Pluid Eilm Lubrication, Theory Design, Cambridge University Press, New York (1998)... 

The effect of plasticizers has been explained by the lubricity, gel, and free volume theories. The lubricity theory states that the plasticizer acts as an internal lubricant and permits the... 

In the past, various resin flow models have been proposed [2,15-19], Two main approaches to predicting resin flow behavior in laminates have been suggested in the literature thus far. In the first case, Kardos et al. [2], Loos and Springer [15], Williams et al. [16], and Gutowski [17] assume that a pressure gradient develops in the laminate both in the vertical and horizontal directions. These approaches describe the resin flow in the laminate in terms of Darcy s Law for flow in porous media, which requires knowledge of the fiber network permeability and resin viscosity. Fiber network permeability is a function of fiber diameter, the porosity or void ratio of the porous medium, and the shape factor of the fibers. Viscosity of the resin is essentially a function of the extent of reaction and temperature. The second major approach is that of Lindt et al. [18] who use lubrication theory approximations to calculate the components of squeezing flow created by compaction of the plies. The first approach predicts consolidation of the plies from the top (bleeder surface) down, but the second assumes a plane of symmetry at the horizontal midplane of the laminate. Experimental evidence thus far [19] seems to support the Darcy s Law approach. 

The viscous dissipation term is normally not important. Its significance has been considered in connection with lubrication theory (VI), flow through tubes (B20), extrusion of plastics melts (BIO), and viscometry in rotating-cylinder systems (W6). There is also an additional contribution to the energy flux vector describing energy transport by radiation. See discussion in connection with Eq. (29). 

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