Diffusion coefficient dilute solution

A useful equation for the calculation of liquid phase diffusivities of dilute solutions of non-electrolytes has been given by Wilke and CHANG(I6). This is not dimensionally consistent and therefore the value of the coefficient depends on the units employed. Using SI units ... 

Jeffrey [181] estimated the effective conductivity in a dilute suspension of spherical particles, and in terms of diffusion coefficient his solution was... 

Die next parameter we need is the diffusion coefficient Df of hydrogen peroxide in water. Here, we can assume the approximate value of 10 9 m2/s. However, this coefficient will be needed further in this example for the determination of the effective solid-phase diffusion coefficient, in a calculation that is extremely sensitive to the value of the liquid-phase diffusion coefficient. For this reason, coefficient should be evaluated with as much accuracy as possible. The diffusion coefficient of solutes in dilute aqueous solutions can be evaluated using the Hayduk and Laudie equation (see eq. (1.26) in Appendix I) ... 

For the determination of diffusion coefficient of solutes (except from salts and ions) in water and dilute solutions (<10%) the Hayduk and Laudie equation is used (Lyman et al., 1990 Perry and Green, 1999) ... 

It is to be hoped that future calculations will attempt to predict the diffusion coefficients of solutes in narrow pores. Measurements in such systems are extremely difficult to carry out and recent experiments in an admittedly broad pore (a 2 mm diameter capillary) are therefore of particular interest. Liukkonen and co-workers [61] found that the diffusion coefficient of NaCl in a dilute aqueous solution was 75% greater at the walls of this capillary than in the bulk solution, a result in line with the phenomenon of "surface conductivity [62]. Yet this finding clearly runs counter to the trend in the self-diffusion calculations in much narrower pores. It rather looks at this stage as if electrolytes near polar walls behave quite differently from non-electrolytes. 

On dissociation of a salt, ions start to diffuse in a solution. Without an electric potential effect, however, the diffusion of a single salt is treated as molecular diffusion. For dilute solutions of a salt, the Nemst-Haskell equation is used to estimate the dilfusivity coefficient... 

Diffusivity data are available only for a limited number of polymer-solvent systems. This paper describes research that has led to the development of the use of capillary column inverse gas chromatography (IGC) for the measurement of diffusion coefficients of solute molecules in polymers at infinite dilution. The work has resulted in a precise, rapid technique for the diffusion measurements that circumvents the many problems attendant to classical sorption methods and packed column IGC methods. Initial results of the program appeared in two recent publications (1,2)- Some of the material introduced in those papers is discussed here to present background for... 

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)] ... 

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. 

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. 

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... 

An electrolyte solution which is not in equilibrium is exposed to generalized forces that are responsible for irreversible processes, such as transport or relaxation processes. A gradient of the chemical potential of the considered ions is the source of such a force, producing a particle flow that leads to diffusion and to electric conductance. Neglecting activity coefficients (dilute solutions) the flow of ion i is given by the relation (with the convection term omitted)... 

Table B-12 Diffusion Coefficients (Aqueous Solutions, Infinite Dilution) ...

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. 

Table 3.A.2. Diffusion coefficients of solute iin a dilute liquid solution, 1 atm at25 C...

This measurement of tracer diffusion in dilute solution is a good strategy. Such a use of radioactive tracers provides a near-unique opportunity for a specific chemical analysis in highly dilute solution. Such analysis is especially important in biological systems, where complex chemistry may compromise analysis. Moreover, in dilute solution, the diffusion coefficients found with radioactive tracers are almost always indistinguishable from those measured in other ways. Exceptions occur in those systems in which the solute moves by a jump mechanism like that for protons (see Fig. 6.1.-1) or in which the solute s molecular weight is significantly altered by the isotopic mass. 

In dilute solutions, tire dependence of tire diffusion coefficient on tire molecular weight is different from tliat found in melts, eitlier entangled or not. This difference is due to tire presence of hydrodynamic interactions among tire solvent molecules. Such interactions arise from tire necessity to transfer solvent molecules from tire front to tire back of a moving particle. The motion of tire solvent gives rise to a flow field which couples all molecules over a... 

Let us now turn attention to situations in which the flux equations can be replaced by simpler limiting forms. Consider first the limiting case of dilute solutions where one species, present in considerable excess, is regarded as a solvent and the remaining species as solutes. This is the simplest Limiting case, since it does not involve any examination of the relative behavior of the permeability and the bulk and Knudsen diffusion coefficients. 

Table 4. Diffusion Coefficients for Dilute Solutions of Gases in Liquids at 20°C ...

The Stokes-Einstein equation has already been presented. It was noted that its vahdity was restricted to large solutes, such as spherical macromolecules and particles in a continuum solvent. The equation has also been found to predict accurately the diffusion coefficient of spherical latex particles and globular proteins. Corrections to Stokes-Einstein for molecules approximating spheroids is given by Tanford. Since solute-solute interactions are ignored in this theory, it applies in the dilute range only. 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

Examples of this procedure for dilute solutions of copper, silicon and aluminium shows the widely different behaviour of these elements. The vapour pressures of the pure metals are 1.14 x 10, 8.63 x 10 and 1.51 x 10 amios at 1873 K, and the activity coefficients in solution in liquid iron are 8.0, 7 X 10 and 3 X 10 respectively. There are therefore two elements of relatively high and similar vapour pressures, Cu and Al, and two elements of approximately equal activity coefficients but widely differing vapour pressures. Si and Al. The right-hand side of the depletion equation has the values 1.89, 1.88 X 10- , and 1.44 X 10 respectively, and we may conclude that there will be depletion of copper only, widr insignificant evaporation of silicon and aluminium. The data for the boundaty layer were taken as 5 x lO cm s for the diffusion coefficient, and 10 cm for the boundary layer thickness in liquid iron. 

The mobility u-can be taken from Table 2-2 for dilute solutions and is proportional to the diffusion coefficient D. It follows, for the transport of anions and cations of an n-n valent salt, that... 

With electrochemical methods such as chronoamperometry, cyclovoltammetry (CV), or conductivity measurements, the diffusion coefficients of charged chemical species can be estimated in highly dilute solutions [16, 17]. 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

Wilke, CR Chang, P, Correlation of Diffusion Coefficients in Dilute Solutions, AlChE Journal 1, 264, 1955. 

In dilute aqueous solutions the diffusion coefficients of most ions and of many neutral substances are similar and have values that at room temperature are within the limits of 0.6 X 10 and 2 X lO cmVs. The values generally exhibit a marked decrease with increasing solution concentration (Fig. 4.1). 

We have applied FCS to the measurement of local temperature in a small area in solution under laser trapping conditions. The translational diffusion coefficient of a solute molecule is dependent on the temperature of the solution. The diffusion coefficient determined by FCS can provide the temperature in the small area. This method needs no contact of the solution and the extremely dilute concentration of dye does not disturb the sample. In addition, the FCS optical set-up allows spatial resolution less than 400 nm in a plane orthogonal to the optical axis. In the following, we will present the experimental set-up, principle of the measurement, and one of the applications of this method to the quantitative evaluation of temperature elevation accompanying optical tweezers. 

Wilke, C. R. and Chang, P. (1955) AIChE Jl 1, 264. Correlation for diffusion coefficients in dilute solutions. 

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