Diffusion constant frictional factor

Thermal diffusivity Temperature sensitivity Temperature difference Thickness of tube Aspect ratio, relation of Cp/Cy Fluid dielectric constant Wall zeta potential Dimensionless temperature Friction factor, Debye length Mean free path Dynamic viscosity Kinematic viscosity Bejan number Density... 

After writing mass balances, energy balances, and equilibrium relations, we need system property data to complete the formulation of the problem Here, we divide the system property data into thermodynamic, transport, transfer, reaction properties, and economic data. Examples of thermodynamic properties are heat capacity, vapor pressure, and latent heat of vaporization. Transport properties include viscosity, thermal conductivity, and diffusivity. Corresponding to transport properties are the transfer coefficients, which are friction factor and heat and mass transfer coefficients. Chemical reaction properties are the reaction rate constant and activation energy. Finally, economic data are equipment costs, utility costs, inflation index, and other data, which were discussed in Chapter 2. 

The proportionality constant D is called the diffusion coefficient (S.I. unit m2-s ). Einstein also derived that D = kBT//, and taking Stokes s expression for the friction factor / for spheres, the relation becomes... 

Here D is the diffusion constant within the tube, and is distinguished from translation outside the tube, which will be slower and more difficult. This can be expressed in terms of the frictional coefficient for the chain,/, again within the mbe confines (Z), = kT . However, because the reptation is assumed to occur by migration of a segmental kink along the chain, the force needed to do this is applied one segment at a time, and so it is more appropriate to use the frictional factor per segment n). Thus,... 

A, B Coefficient in Equation 17 D Diameter, m D Diffusivity, mVs De Dean number. Re (D/D ) , dimensionless f Fannings friction factor, dimensionless K, Constants in Equation 52 p Pitch, m r Radius, m Re Reynolds number VDp/p, dimensionless Sc Schmidt number p/pD, dimensionless V Velocity, m/s... 

In chemical kinetics the concept of the order of a reaction forms the basis of a kinematics which constitutes a frame for most of the molecular theories of chemical reactions. The fundamental magnitudes of this kinematics are the concentrations and the specific rate constants. In simple cases only the time enters as an independent variable, whereas in a diffusion process both time and space are involved. Diffusion processes are generally described in terms of diffusion coefficients, volume concentrations and thermodynamic potential or activity factors. Partial volume factors and friction coefficients associated with the components of the diffusing mixture are also essential in the description. A feature of the macro-dynamical theory is that it covers any region of concentration. Especially simple equations are connected with the differential diffusion process (diffusion with small concentration differences), for which the different coefficients or factors mentioned above are practically constant. 

If equilibrium solvation is the only cause of the solvent effect then the Mu reaction should also be a factor 35 faster in aqueous solution compared to the gas phase. This was not observed, the increase of its rate constant in water for addition to benzene amounts to only a factor of 3-5 (Figure 8), and it is not limited by diffusion. The difference was ascribed to a dynamic solvent effect and taken as evidence of Kramers solvent friction which increases with frequency and is thus obviously far more important for the reaction of Mu, the lighter isotope [33]. 

Skewis [89] measured the tack of rubber to rubber and rubber to glass as a function of contact time and results are shown in Fig. 19. The two factors which might contribute to tack in this case are the development of intimate contact by viscous flow of the polymer, and diffusion of polymer segments across the interface. Diffusion will not occur between polymer and glass, and the low levels of tack which develop between styrene-butadiene rubber and butyl rubber indicate low levels of diffusion. Higher levels of autohesion develop with the like polymer pairs and this was attributed to diffusion across the interface. As both viscous flow and diffusion are controlled by the same friction constant, factors which change D... 

The first question to be asked is why the Brownian diffusion model of Kirkwood should give reasonable results for the unlike-ion friction constants, as mentioned in Section 3.4, when the Coulomb potential is ignored and the experimental radial distribution function used. The assumptions in the Brownian diffusion model are difficult to evaluate but Douglass et have shown it to be a factor of njl greater than their result using a Gaussian autocorrelation function. Now from molecular dynamics Alder et have shown for hard spheres at high densities that the autocorrelation... 

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