Diffusion constant viscosity effects

Here, D is the diffusion constant for heat or material and the kinematic viscosity of the liquid. A consequence of the existence of such a diffusive surface barrier is that the diffusion length = D/F is to be replaced by in all formulas, as soon as growth rate V the more important become the hydrodynamic convection effects. 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

Deacon s intention was to separate the viscosity effect from the wind effect, so that the new model would be able to describe the change of via due to a change of water or air temperature (i.e., of viscosity) at constant wind speed. Deacon concluded that mass transfer at the interface must be controlled by the simultaneous influence of two related processes, that is, by the transport of chemicals (described by molecular diffusivity Dia), and by the transport of turbulence (described by the coefficient of kinematic viscosity va). Note that v has the same dimension as Dia. Thus, the ratio between the two quantities is nondimensional. It is called the Schmidt Number, Scia ... 

The entry-length region is characterized by a diffusive process wherein the flow must adjust to the zero-velocity no-slip condition on the wall. A momentum boundary layer grows out from the wall, with velocities near the wall being retarded relative to the uniform inlet velocity and velocities near the centerline being accelerated to maintain mass continuity. In steady state, this behavior is described by the coupled effects of the mass continuity and axial momentum equations. For a constant-viscosity fluid,... 

C olvents have different effects on polymerization processes. In radical polymerizations, their viscosity influences the diffusion-controlled bimolecular reactions of two radicals, such as the recombination of the initiator radicals (efficiency) or the deactivation of the radical chain ends (termination reaction). These phenomena are treated in the first section. In anionic polymerization processes, the different polarities of the solvents cause a more or less strong solvation of the counter ion. Depending on this effect, the carbanion exists in three different forms with very different propagation constants. These effects are treated in the second section. The final section shows that the kinetics of the... 

An interesting aspect of Eq. (8) was discussed by Jumars et al. (1993). The only factor directly influenced by temperature is the diffusion constant D, which is a function of water viscosity. The temperature dependence of this physical process is less than the Q10 of 2.7-3 normally found for biological processes. In our expression for BCD [Eq. (2)], however, such an argument would apply to both aB in the numerator and aA in the denominator the effect on affinity constants would therefore be expected to cancel out. From the preceding arguments, clearance rates and affinity constants... 

The auto-hydrolytic effect of boiling an aqueous solution was also investigated by following changes in the sedimentation and diffusion constants and the intrinsic viscosity. Although the measurements were complicated by the fact that the insoluble portion dissolved as boiling proceeded, the results indicated that the gum molecules were long chains with small adjacent side chains, and that hydrolysis attacked the weaker side chains. 

In an extended series of studies, we have shown that Vs(r) and the quantities that we use to characterize it provide an effective means for analyzing noncovalent interactions and predicting quantitatively the values of properties that depend upon them, such as boiling points and critical constants, heats of phase transitions, solubilities and solvation energies, partition coefficients, diffusion constants, surface tensions, viscosities, etc. This work has been reviewed on several occasions.48-50... 

The effective viscosity of the solvent at the protein surface is likely greater than the bulk solvent viscosity. The diffusion constant of water at the protein surface is five times smaller than the bulk water value (Polnaszek and Bryant, 1984a). This effect probably can be neglected in experiments such as those discussed in the previous paragraphs, which cover several orders of magnitude in solvent viscosity. 

It is pertinent to consider separately the enhancement effect of salt on two steps the initiation step (onset of the flow) and the structured flow. The transport rates are related to the properties of the final structured flow and are contributed from the effects on both steps. The effect on the initiation step is clearly noticed since the critical PVP concentrations for the occurrence of the structured flow depended on the kind of salt. Effects of a salt on the cross diffusion constants of the two polymer components will be examined on both excluded volume and frictional effect. The effect on the excluded volume interaction between the two polymer components is expected to be small. This expectation is partly supported by the result that coil dimension of PVP was not influenced by the addition of a salt at 2 M in the cases of three salts LiCl, NaCl and CsCI, while these salts showed quite diverse effects on the trrmsport rates of PVP. Since viscosities vary with the kind and the concentration of salt, frictional coefficients are influenced by the presence of a salt. In this respect cross diffusion constants may be affected by salt through a change in viscosity of the medium. 

These last two equations are derived on the basis of the Eyring theory of holes in liquids. The assumptions here, in contrast to those of the Stokes-Einstein equations, are that the diffusing molecules are of the same order of size as those of the solvent. The discontinuity of the liquid medium thus plays an essential part in the Eyring theory, the fundamental length X being the distance between successive positions of the diffusing solute or solvent molecule as it jumps between the molecules of the liquid. The quantities D and )/, however, refer to the diffusion constant and the viscosity of the system measured in the usual way. They represent the observed effect of very large numbers of such molecular jumps. 

It has been our experience that 7s(r) and Vs(r) play different but complementary roles with respect to molecular reactivity [71,83-85], Vs(r) is effective for treating noncova-lent interactions, which are primarily electrostatic in nature [74,86-89], For instance, a variety of condensed-phase physical properties - boiling points, critical constants, heats of phase transitions, solubilities and solvation energies, partition coefficients, surface tensions, viscosities, diffusion constants and densities - can be expressed quantitatively in terms of one or more key features of Vs(r), such as its maximum and minimum, average deviation, positive and negative variances, etc. [80,90-92], Hydrogen bond donating... 

It has also been shovm that the diffusion coefficients in a solvent are inversely proportional to its viscosity. The viscosity changes with temperature, composition, and the concentration of the feed. When the column is operated at a constant reduced velocity, v = udp)/Dj, the efficiency constant. The effect of a change of viscosity due to an adjustment in any of the parameters just Hsted will have Ht-tle effect on the pressure required to keep the reduced velocity constant (since the product of the viscosity and the diffusion coefficient remains constant) but it will markedly affect the retention times (which will increase with increasing viscosity) and, in preparative applications, the production rate. Thus, conditions under which the viscosity is low should be preferred. 

The diffusion coefficient varies with both temperature and pressure and is strongly influenced by density and viscosity [2]. Density and viscosity both increase with pressure with a corresponding decrease in the diffusion coefficient. The effect is less pronounced at higher pressure because density becomes less sensitive to pressure. The diffusion coefficient generally increases with temperature at constant pressure. However, at constant density, temperature appears to have a minimal effect. 

The onset of crystallization in the Vitreloy 1 alloy shown in Fig. 1.3 was based on the detection of a crystalline volume fraction of 10 " by conventional methods. There are two different curves for the onset of crystallization in Fig. 1.3. For the solid curve, which was obtained using classical nucleation theory, the effective diffusion constant was taken to be proportional to the reciprocal of the viscosity, which was considered to be of the VFT form. The dotted curve was obtained by the use of an Arrhenius form of expression for the effective diffusion constant, which was found to fit better at lower temperatures near Tg (Masuhr et al. 1999). This discussion shows that for understanding the kinetics of crystallization in multi-component alloys considerable improvisation becomes necessary. 

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