Friction coefficient for

Another, purely experimental possibility to obtain a better estimate of the friction coefficient for rotational motion in chemical reactions consists of measuring rotational relaxation times of reactants and calculating it according to equation (A3,6,35) as y. =... 

Table 3. Correlations for Convective Heat-Transfer and Friction Coefficients for Circular Tube Flow ...

Table 5. Correlations for Heat-Transfer and Darcy Friction Coefficients for Noncircular Laminar Duct Flow ...

The spreading rate of a polymer droplet on a surface has been measured (363,364). The diffusion constant was at least an order of magnitude smaller than that of the bulk. The monomer—surface friction coefficient for polystyrene has been measured on a number of surfaces and excellent... 

Friction and Adhesion. The coefficient of friction p. is the constant of proportionality between the normal force P between two materials in contact and the perpendicular force F required to move one of the materials relative to the other. Macroscopic friction occurs from the contact of asperities on opposing surfaces as they sHde past each other. On the atomic level friction occurs from the formation of bonds between adjacent atoms as they sHde past one another. Friction coefficients are usually measured using a sliding pin on a disk arrangement. Friction coefficients for ceramic fibers in a matrix have been measured using fiber pushout tests (53). For various material combinations (43) ... 

Fig. 39—Friction coefficient for different concentrations [60], Load 2 N, Base oil PEG, Sliding speed 2 mm s h...

Frictional coefficient for an element, or bead, of the polymer chain (Chap. XIV). 

BK Fritzinger, SK Bauman, DJ Lyman. Membrane characteristics, permeability parameters, and frictional coefficients for cupraphane. J Biomed Mater Res 5 3-16, 1971. 

Figure 21 Friction coefficient for differently oriented Ni(100)/Ni(100) interfaces. Rough surfaces have a 0.8 A rms variation in roughness added to the atomically smooth surfaces. Reproduced with permission from Ref. 85.

The friction coefficient for X-750 appears to trend upward as the environment is changed from vacuum to pure N,to a 4% dilute H2 mixture, as shown in Fig. 7. The measured surface roughness of the worn surfaces was 3.8 pm Sa. 

This approximation is equivalent to assuming that the differences in internal densities and, consequently, in solvent draining, between a branched chain and the homologous linear chain, when included in their corresponding mean sizes, can describe both the friction coefficient and the viscosity. Besides these theoretical considerations, an empirical correlation in terms of a log-log fit of h vs f was employed by Roovers et al. [51]. Kurata and Fukatsu [48] and Ptitsyn [82] performed a more general Kirwood evaluation of the friction coefficient for different types of ideal branched molecules (uniform and randomly distributed stars, combs and random-branched structures). Their results for different structures are included within the limits l[Pg.60]

Fig. 3.8 Temperature dependence of the monomeric friction coefficients for PEP and PE. The symbols present the NSE results (filled triangle PEP, filled circle PE). The solid lines display the respective rheological predictions extrapolations are shown as dashed lines (solid lines prediction [51],point dashed line prediction [34] for PEP)...

Cartesian kinetic SDEs with unprojected, geometrically projected, and inertially projected random forces require the same correction forces in certain special cases. Inertial and geometric projections are completely equivalent for models with an equal bead mass m for all beads, for which the mass tensor m v = is proportional to the identity. Unprojected and geometrically projected random forces require identical correction forces in the case of local, isotropic friction with an equal friction coefficient for all beads, as in the Rouse or Kramers model, for which the friction tensor ... 

Table E4.4.1 Boundary layer thickness and skin friction coefficient for aflat plate moving at 20 m/s in the atmosphere...

Recall also from Section 4.1.5 that many biological molecnles in solution are not spherical, and can be modeled as either prolate or oblate ellipsoids (see Figure 4.17). A further factor affecting diffnsion of these ellipsoids in dilnte aqneous solutions is that the molecnles can become solvated, resulting in an effective radins that is different than the nnsolvated molecnles. These concepts of asymmetry and solvation are illnstrated in Fignre 4.57. Accordingly, there are friction coefficients for the unsolvated Stake s... 

Fig. 7 Multivariate plot of wear rate versus friction coefficient for various unfilled polymers, polymer blends, and polymer composites...

Some narrowing of the spectrum does occur when there is a strong positional dependence in the frictional coefficient. For example, the reduced compliance is ... 

Thus the relaxation spectrum resulting from the average coordinates equation11 of our model has the same form as that of Rouse, of Kargin and Slonimiskii, or of Bueche. In order to relate the parameters of the model to those of the Rouse theory, the time scale factor a must somehow be connected to the frictional coefficient for a single subchain of a Rouse molecule. To achieve this comparison, we may23 study the translational diffusion coefficients as computed for the two models. 

Electrophoretic mobility (pep) s the constant of proportionality between the speed of the ion and the strength of the electric field. Mobility is proportional to the charge of the ion and inversely proportional to the friction coefficient. For molecules of similar size, the magnitude of the mobility increases with charge ... 

The peculiarity of this expression, however, is that it does not make sense for dilute solutions of Gaussian coil molecules. In fact, the free-draining case is characterized by the limit of infinetely smaE friction coefficient . For this case, the contributions of the chain molecules to the viscosity of the solution becomes zero. 

So he calculated on the basis of experiments of Stewart and Gray-don (167) the ratio of "reduced friction coefficients for membranes... 

Example 11.4. McGuiggan et al. [492] measured the friction on mica surfaces coated with thin films of either perfluoropolyether (PFPE) or polydimethylsiloxane (PDMS) using three different methods The surface forces apparatus (radius of curvature of the contacting bodies R 1 cm) friction force microscopy with a sharp AFM tip (R 20 nm) and friction force microscopy with a colloidal probe (R 15 nm). In the surface force apparatus, friction coefficients of the two materials differed by a factor of 100 whereas for the AFM silicon nitride tip, the friction coefficient for both materials was the same. When the colloidal probe technique was used, the friction coefficients differed by a factor of 4. This can be explained by the fact that, in friction force experiments, the contact pressures are much higher. This leads to a complete penetration of the AFM tip through the lubrication layer, rendering the lubricants ineffective. In the case of the colloidal probe the contact pressure is reduced and the lubrication layer cannot be displaced completely. 

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