Friction coefficient 390 Subject

This expression shows diat if die detuning Acuj is negative (i.e. red detuned from resonance), dieii die cooling force will oppose die motion and be proportional to die atomic velocity. The one-diniensional motion of die atom, subject to an opposing force proportional to its velocity, is described by a damped haniionic oscillator. The Doppler damping or friction coefficient is die proportionality factor. 

Fig. 3.1 Bead-spring-bead model of a Gaussian chain as assumed in tbe Rouse model. Tbe beads are connected by entropic springs and are subject to a frictional force where v is the bead velocity and fo the bead friction coefficient...

Hydration is a complex phenomena influenced by intrinsic (i.e., age, anatomical site) and extrinsic (i.e., ambient humidity, chemical exposure) factors. These factors can affect the mechanical properties of the skin and research has been performed to correlate hydration levels with the skin s friction coefficient.24 Hydration studies have investigated how increases and decreases in skin hydration correlated with the friction coefficient. In past studies researchers generally induced increases in skin hydration through water exposure. However, decreases in skin hydration were not experimentally induced and dehydration studies were performed between subjects with normal skin and subjects that had clinically dry skin.2 12... 

FIGURE 32.3 Effect of lubricant cosmetic ingredient on skin friction coefficient. Amount applied of each material 2 mg/cm2. Reproduced from Nacht et al.14 (mean of five subjects but P value was not published). Time = — 1 is immediately prior to application Time = —0 is immediately after application. 

FIGURE32.4 Correlation between changes in the friction coefficient and the sensory perception of greasiness. A, B, C, D, E, and F represent different creams that were applied to the skin. The reported percent change in the friction coefficient is immediately after application and the greasiness scores were subjective evaluations. Reproduced (from Nacht et al.14). 

Once the average friction coefficient C is available, the drag (or friction) force over the surface can be determined from Rq. 7-1. In this case/1 is the surface area of the plate exposed to fluid flow. When both side.s of a thin plate are subjected to flow, A becomes the total area of the top and bottom surfaces. Note that the friction coefficient, in general, varies with location along the surface. 

SOLUTION A liquid mixture flowing in a tube is subjected to uniform wall heat flux. The friction coefficients are to be determined for the bell-mouth and square-edged inlet cases. 

The simplest way to correct viscosity data to constant friction coefficient is to first fit the temperature dependence of viscosity of each individual sample to the WLF equation [Eq. (8.134)], which determines 5//q. At a given reference temperature, sufficiently long chains have the same 5//o and progressively lower values of 5//o are obtained for shorter chains, since they have more free volume at a given temperature. The viscosity data at the reference temperature can then be corrected to the friction coefficient of the long chains at the reference temperature using Eq. (8.133). Viscosity data subjected to such a correction are shown in Fig. 8.17 for polybutadiene, polyisobutylene and polystyrene, roughly... 

In summary, Eq. (A.31) validly describes the long time motions of particles with sufficiently large friction coefficients (per unit mass) /M, subject to sufficiently weak forces (per unit mass) Fg/M. 

A polymer ehain can be approximated by a set of balls connected by springs. The springs aeeount for the elastic behaviour of the chain and the beads are subject to viscous forces. In the Rouse model [35], the elastic force due to a spring connecting two beads is/= bAr, where Ar is the extension of the spring and the spring eonstant is h = T/a ffpis the root-mean-square distance of two successive beads. The viseous foree that acts on a bead is the produet of the bead velocity u and of the friction coefficient of a bead. With these assumptions, one finds for... 

Note that, in addition to translational motion, other kinds of motion will be subject to random thermal fluctuations as well. In particular, the tumbling of (macro)molecules in solution can be described in terms of rotational diffusion, for which equivalent rotational diffusion constants can be defined. By analogy with translational diffusion described above, the rotational diffusion coefficient (/>rot) and rotational friction coefficient (/rot) are related by the expression ... 

Concentration Dependence of Df. The concentration dependence of the frictional coefficient of macromolecules in dilute solution is another aspect which has recently been the subject of theoretical and experimental activity and which is quite sensitive to the details of hydrodynamic structure of individual particles. 

Die compaction of agglomerates has been simulated in a computer sphere model by Thornton et When the particles are in a liquid paste, the liquid is usually expelled through pores in the mold, and the partieles form a filter cake. The mechanism by which this occurs has been modeled by Woodcock et The application of forces to powder beds, sometimes immersed in liquids, is the subject of soil mechanics. " This considers particles to interact via Coulomb s law, Equation (11.16), but also takes into account the hydrodynamic forces acting on the individual particles. Unfortunately, as we have seen. Coulomb s law is not correct for particles which experience molecular adhesion, so the friction coefficients found in soil mechanics theories seem to vary. Friction seems to increase as the particles get smaller because smaller particles adhere more strongly. Soil mechanics is therefore a difficult science. 

There is scattered evidence in the literature which shows that Amontons classical laws frequently do not apply to solid film lubricants in load ranges of practical importance. This subject has been reviewed elsewhere . The failure of these classical laws has recently been demonstrated for several polymer films by Towle " and Bowers It has been found that for both organic and inorganic solid film lubricants the friction coefficient decreases markedly with increasing load approaching a small asymptotic value at very high loads. The decrease observed is sometimes as much as an order of magnitude. 

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