Frictional coefficient, diffusional

C[, corresponding to the Stokes diffusional process, can be written as the product of the Stokes friction coefficient multiplied by a correcting factor fr taking into account the finite thickness of the solvent layers... 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

For non-spherical particles the friction coefficient, B, depends on both particle size and shape, for which reason the use of any one, either diffusional or sedimentation, method yield only some conditional particle radius corresponding to that of a spherical particle with the same sedimentation or diffusion coefficient. The values of such equivalent radii may differ, depending on which experimental method was used for their assessment. To determine the true particle size or mass, m, of non-spherical particles, and to obtain the information regarding particle shape, one must perform an independent determination of the sedimentation coefficient and friction factor... 

EXAMPLE 18.6 Autocorrelation times. The correlation time m/ is the time required for the velocity autocorrelation function to reach 1/e of its initial value. The correlation time is short when the mass is small or when the friction coefficient is large. The correlation time for the diffusional motion of a small protein of mass m = 10,000 g moP is in the picosecond time range (see Equation (18.56)) ... 

Figure 3.5 Rotational diffusional motion of ellipsoids in liquids. The ratio of the friction coefficients calculated using slip boundary conditions to that calculated using stick boundary conditions, for prolate ellipsoids and for oblate ellipsoids, plotted against a/b, the ratio of the shorter axis to the longer axis. From Ref. [1 l,b].

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

We have carried out a wide range of studies concerned with the dextran concentration dependence of the transport of the linear flexible polymers and have varied both molecular mass and chemical composition of this component. Moreover, we have studied the effect of the variation of the molar mass of the dextran on the transport of the flexible polymers 51). In general, the transport of these polymers in dextran solutions may be described on common ground. At low dextran concentrations the transport coefficients of the polymers are close to their values in the absence of the dextran and may even exhibit a lower value. This concentration range has been discussed in terms of normal time-independent diffusional processes in which frictional interactions predominate. We have been able to identify critical dextran concentrations associated with the onset of rapid transport of the flexible polymers. These critical concentrations, defined as C, are summarized in Table 1. They are... 

The Stokes equation gives the friction constant of a rigid sphere with radius S as 6n S (where n is the viscosity coefficient of the liquid surrounding Bhe sphere) The diffusional velocity of a sphere is proportional to the inverse of the friction constant. The Inverse of the viscosity coefficient of the original solution, 1/n, is expressed by k exp(-AF /kT) (where k is a constant... 

Errors are inherent in the above solutions because of the uncertainties in the transport properties of air at very high temperatures. The theories of Refs. 15 and 17 employed total properties from different sources, while Ref. 16 accounted for equilibrium air by using frozen properties and Le = 1 in the diffusional heat flux contribution. A comparison of skin friction and heat transfer coefficients reveals differences of less than 10 percent between the results of Refs. 15 and 16 and only a few percent between the results of Refe. 16 and 17. Thus, prior to ionization the errors in convective heating predictions caused by property uncertainties are rather small. With the onset of ionization, large errors may have been introduced because of the large uncertainty of the thermal conductivity of ionized air as influenced primarily by the charge-transfer cross section of atomic nitrogen. Hence, the marked increase in heat transfer rate with the presence of ionization [17] can only be considered qualitatively correct. 

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