Diffusion in dilute solutions

Fig. 45a, b. Segmental diffusion in dilute solutions at the crossover from - to good solvent conditions. Reduced characteristics frequencies Qred (Q,x) vs. x = (T — )/ at different Q-values a PDMS/d-bromobenzene b PS/d-cyclohexane. (b reproduced with permission from [115]. Copyright 1980 The American Physical Society, Maryland)... 

Values of diffusivity in gas mixtures at normal temperature and atmospheric pressure are in the approximate range of 0.03-0.3 m- h and usually increase with temperature and decrease with increasing pressure. Values of the liquid phase diffusivity in dilute solutions are in the approximate range of 0.2-1.2 X 10 5 m h , and increase with temperature. Both gas-phase and liquid-phase diffusivities can be estimated by various empirical correlations available in reference books. 

The semidilute diffusion coefficient can be written in terms of the Zimm diffusion coefficient of the chain Dz [Eq. (8.23) valid for diffusion in dilute solutions] and the overlap concentration (f> [Eq. (5.19)] ... 

Comparison of polymer and solvent diffusion in dilute solution. 

Membrane Diffusion in Dilute Solution Environments. The measurement of ionic diffusion coefficients provides useful information about the nature of transport processes in polymer membranes. Using a radioactive tracer, diffusion of an ionic species can be measured while the membrane is in equilibrium with the external solution. This enables the determination of a selfdiffusion coefficient for a polymer phase of uniform composition with no gradients in ion or water sorption. In addition, selfdiffusion coefficients are more straightforward in their interpretation compared to those of electrolyte flux experiments, where cation and anion transport rates are coupled. 

Appendix 7. A The Coupling Between Translational and Rotational Diffusion in Dilute Solution, 149... 

APPENDIX 7.A THE COUPLING BETWEEN TRANSLATIONAL AND ROTATIONAL DIFFUSION IN DILUTE SOLUTION... 

The coefficient multiplying the Reynolds number for a straight channel is 0.16 (Schlichting 1979). Therefore, for a Reynolds number based on a channel width 2h) of 1000, the Poiseuille profile would develop in about 40 channel widths. Again, since v> D for diffusion in dilute solution, we may expect that the development length is very much longer for the concentration profile than for the velocity profile. 

According to Nemst-Einstein equation (e.g., Daniels and Alberty, 1955), the diffusivity is proportional to temperature for diffusion in dilute solution. The diffusivity at T = 60°C are about 4 times of the values at T = 15°C. The decrease of the effect aperture by 30% implies that the proportionality k in the linear relation is increased by 30%. We then have P = 3900r for 60°C. Four times increase of D implies only two times of increase of /rsince k -Jd... 

Shrier, 1967 (16) recommended equations (1.18) and (1.20) to estimate liquid diffusivities in dilute solutions. 

Equimolar counterdiffusion and/or diffusion in dilute solutions. Equation (10.4-2) holds for equimolar counterdiffusion, or when the solutions are dilute, Eqs. (10.4-8) and (10.4-2) are identical. 

Fluctuations in ion density near a polyelectrolyte impose fluctuating electrostatic forces on the chain that can affect the chain s diffusion. As described by Sedl (207), polyelectrolyte diffusion in dilute solution is fast diffusion because coim-terions cause more rapid motion in a polyelectrolyte than would be noted in an equivalent neutral chain. Several investigators have modified equation 50 to include this Nernst-Hartley-type diffusion in a consistent manner (203,206). Tivant and co-workers suggested that in a monovalent electrolyte solution at large I the enhancement of Dm by polyelectrolyte-electrolyte coupling should be expressed as(208)... 

These three formulae apply in their present form to zeolitic diffusion in dilute solution, or to place exchange diffusion. In concentrated zeolitic solution No. of vacant interstices. . . , ... 

The correlations discussed earlier pertain to diffusion in dilute solutions. With increased concentration, some things are different and the considerations will thus be different. Diffusion coefficients vary with the volume fraction of the solute, often in a complex manner with extrema. Diffusion coefficients are no longer a proportionality constant, but vary with concentration and become concentration... 

From Eq.5.36 it is seen that Nd does not enter into the expression for the diffusion coefficient for interstitial diffusion in dilute solutions, thus in this case the activation energy, Q, represents that of the mobility of the diffusing interstitial atoms AHni= Q. 

The depolarized scattering is related to orientation fluctuations, thereby being determined by rotational diffusion in dilute solutions, but dependent on translational modes as well in moderately concentrated solutions. In general,... 

This equation is typically used for diffusion in dilute solutions, and it is similar to equations used in momentum (Table 2.9 or Eq. 5.58) and heat transfer (Table 5.3 or Eq. 5.59). Table 4.5 summarizes the expressions for Eq. 4.30 for the three coordinate systems. Division of all terms of Eq. 4.30 by the molecular weight of A gives the forms of the continuity equation shown in Table 4.6. Finally, note that the left side of Eq. 4.30 can be written as B(pa)/Dt, where D/Bt notes the material derivative. 

Second and more important, diffusion in dilute solutions is easier to understand in physical terms. A diffusion flux is the rate per unit area at which mass moves. A concentration profile is simply the variation of the concentration versus time and position. These ideas are much more easily grasped than concepts Hke momentum flux, which is the momentum per area per time. This seems particularly true for those whose backgrounds are not in engineering, those who need to know about diffusion but not about other transport phenomena. 

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