Friction coefficient, local

Obviously, when the local friction coefficient C = C is a constant, Eq. (44) takes the form of the Nernst-Planck equation. 

Subslituting into its definition gives the local friction coefficient. 

Velociry boundary layer thickness Local friction coefficient ... 

The average friction coefticienl over a surface is delemuDed by integrating the local friction coefficient over the entire surface. 

Based on analysis, the boundary layer thickness and the local friction coefficient at location x for laminar flow over a flat plaie were dcierntined in Chapter 6 to be... 

This permits the local friction coefficient at the cylinder wall to be calculated as... 

Formulas for friction coefficients. Let us introduce the following dimensionless friction coefficients the local friction coefficient... 

For weakly nonlinearly viscous fluids that obey the viscous friction law t = r(7), the local friction coefficient can be found by using the approximate formulas... 

The local friction coefficient is the same for all motions underlying the viscoelastic property of interest. 

Hydrodynamic resistance to the motion of the dispersed (spherical) particles from the continuum solvent is generally taken into account through a local friction coefficient... 

The velocity boundary layer is important in establishing surface frictional effects, such as local friction coefficient Cf. 

It follows that an additional reduction of the data can be made to take into account the effect of temperature on network spacing as well as the local friction coefficient by plotting 1( Jp against log The data of Fig. 11-16 are shown... 

FlG.l 1-17. Data of Fig, 11-16 reduced for the effect of temperature on entanglement coupling spacing, as measured by f, in addition to its effect on the local friction coefficient, as measured by... 

To show the effect of diluent o.n the detailed shapes of viscoelastic functions, it is convenient to employ corresponding-state plots as in Section C of Chapter 12. For the relaxation spectrum, we plot log H - log Tc/Mq against log t - log a o/kT). Of course, for a single polymer and its solutions the only variables are fo and c (which in the pure polymer becomes p). In Fig. 17-9, poly(vinyl acetate) is compared in this manner with its 50% solution in tri-m-cresyl phosphate. The values of log fo at 40°C for these two systems are 1.75 and -5.25, respectively—the diluent reduces the local friction coefficient by a factor of 10. The curves after reduction coincide at the bottom of the transition zone because this is fixed by the corresponding-state conditions, and are rather similar in shape throughout. However, the diluent causes the spectrum to rise somewhat more sharply from the theoretical slope of -5 at short times but at still shorter times it crosses the spectrum of the pure polymer, and its entrance into the glassy zone involves a broader maximum than the latter. 

T is the shortest Rouse relaxation time, which is related to the local friction coefficient experienced by short chain segments. N, is the number of bonds per chain, and Ne is the number of bonds per entanglement. 

If we assume for the moment that this local friction coefficient in our polymer melt is independent of the concentration of the long chains, (as suggested by experimental data ) then the only parameter in Equation 10 which depends upon that concentration will be Ne Theoretical arguments, based largely on dimensional analysis, have produced exponents... 

Figure 9 shows the lubricant film shear stress field, t(x), and local friction coefficient /j(x), calculated in at same point of the gear meshing line (point A) and for the same operating conditions. The global friction coefficient at point A (/UgA) is about 0.03. 

The local lubricant film breakdown, promotes an increase in the local friction coefficient caused by metal/metal contact, which is extended to the global friction coefficient. Being so, the probability of lubricant film breakdown is strong for high loads and speeds. It s clear that local criteria for lubricant film breakdown must be developed and introduced into the mixed film lubrication model. 

Figure 4. Triboscopic images obtained from a Dual Zone Friction Test under unlubricated conditions a) local friction coefficient b) local ECR (test conditions amplitude 2.4 mm, 100 cycles, max. contact pressure 0.5 GPa, ambient air).

A description equivalent to equation (75) introduces a phenomenological non-local friction coefficient f(fe) (in Fourier space) between monomer and solvent. This non-local friction coefficient is such that — Z(/c) = c (fe). In the limit of large wavevectors, 2(fc), and thus f(/c), reaches a finite value f, which represents the effective friction between a given monomer and the solvent. 

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