Solute diffusion-dispersion

Solute Diffusion-Dispersion Coefficient. In these studies D was assumed to be constant and not a function of flow velocity. For low flow velocities this assumption seems reasonably valid (23). For the natural rainfall conditons of these studies the flow velocities were generally quite low. In lieu of actual measured D values on the two Maui soils, an estimate of D obtained on a somewhat similar soil on Oahu bv Khan (24) was used in this study. An average value of D = 0.6 cm /hr was measured in the field with a steady water flux of 10 cm/ day. 

In a packed column, however, the situation is quite different and more complicated. Only point contact is made between particles and, consequently, the film of stationary phase is largely discontinuous. It follows that, as solute transfer between particles can only take place at the points of contact, diffusion will be severely impeded. In practice the throttling effect of the limited contact area between particles renders the dispersion due to diffusion in the stationary phase insignificant. This is true even in packed LC columns where the solute diffusivity in both phases are of the same order of magnitude. The negligible effect of dispersion due to diffusion in the stationary phase is also supported by experimental evidence which will be included later in the chapter. 

The effect is much less when the fluid is a gas, where the solute diffusivity is high and the solute tends to diffuse rapidly across the tube and partially compensate for the nonlinear velocity profile. However, when the fluid is a liquid, the diffusivity is five orders of magnitude less and the dispersion proportionally larger. 

C. In their first series of experiments, six data sets were obtained for (H) and (u), employing six solvent mixtures, each exhibiting different diffusivities for the two solutes. This served two purposes as not only were there six different data sets with which the dispersion equations could be tested, but the coefficients in those equations supported by the data sets could be subsequently correlated with solute diffusivity. The solvents employed were approximately 5%v/v ethyl acetate in n-pentane, n-hexane, n-heptane, -octane, -nonane and n-decane. The solutes used were benzyl acetate and hexamethylbenzene. The diffusivity of each solute in each solvent mixture was determined in the manner of Katz et al. [3] and the values obtained are included... 

In order to relate the value of (H) to the solute diffusivity and, consequently, to the molecular weight according to equation (11), certain preliminary calculations are necessary. It has already been demonstrated in the previous chapter (page 303) that the dynamic dead volume and capacity ratio must be used in dispersion studies but, for equation (11) to be utilized, the value of the multipath term (2Xdp) must also be... 

Thus, a practical procedure would be as follows. Initially the HETP of a series of peptides of known molecular weight must be measured at a high mobile phase velocity to ensure a strong dependence of peak dispersion on solute diffusivity. 

The multipath dispersion on a thin layer plate is the process most likely to be described by a function similar to that in the van Deemter equation. However, the actual mobile phase velocity is likely to enter that range where the Giddings function (3) applies. In addition, as the solvent composition is continually changing (at least in the vast majority of practical applications) the solute diffusivity is also altered and thus, the mobile phase velocity at which the Giddings function applies will vary. 

HETP of a TLC plate is taken as the ratio of the distance traveled by the spot to the plate efficiency. The same three processes cause spot dispersion in TLC as do cause band dispersion in GC and LC. Namely, they are multipath dispersion, longitudinal diffusion and resistance to mass transfer between the two phases. Due to the aforementioned solvent frontal analysis, however, neither the capacity ratio, the solute diffusivity or the solvent velocity are constant throughout the elution of the solute along the plate and thus the conventional dispersion equations used in GC and LC have no pertinence to the thin layer plate. 

The water solubilities of the functional comonomers are reasonably high since they are usually polar compounds. Therefore, the initiation in the water phase may be too rapid when the initiator or the comonomer concentration is high. In such a case, the particle growth stage cannot be suppressed by the diffusion capture mechanism and the solution or dispersion polymerization of the functional comonomer within water phase may accompany the emulsion copolymerization reaction. This leads to the formation of polymeric products in the form of particle, aggregate, or soluble polymer with different compositions and molecular weights. The yield for the incorporation of functional comonomer into the uniform polymeric particles may be low since some of the functional comonomer may polymerize by an undesired mechanism. 

It is seen that when operating at the optimum velocity that provides the minimum value of (H) and thus, the maximum efficiency, solute diffusivity has no effect on solute dispersion and consequently, the column efficiency is independent of temperature. 

It can be noted that in general this result predicts that the ratio of the dispersion coefficient to the free-solution diffusion coefficient is different from the ratio of the effective mobility to the free-solution mobility. In the case of gel electrophoresis, where it is expected that the (3 phase is impermeable (i.e., the gel fibers), the medium is isotropic, and the a phase is the space between fibers, the transport coefficients reduce to... 

Solution-diffusion tubing, flow through, 15 722, 723 Solution dumps, 9 797 Solution/electrode interface, 9 574-581 Solution-enhanced dispersion by... 

The root time method of data analysis for diffusion coefficient determination was developed by Mohamed and Yong [142] and Mohamed et al. [153]. The procedure used for computing the diffusion coefficient utilizes the analytical solution of the differential equation of solute transport in soil-solids (i.e., the diffusion-dispersion equation) ... 

In 1961, Giddings (1) developed an HETP equation of which the Van Deemter equation appeared to be a special case. Giddings was dissatisfied with the Van Deemter equation insomuch that it predicted a finite contribution to dispersion independent of the solute diffusivity in the limit of zero mobile phase velocity. This concept, not surprisingly, appeared to him unreasonable and unacceptable. Giddings developed the following equation to avoid this irregularity. 

The expression for the maximum permissible detector dispersion, given by equation (21), also shows it s strong dependance on the product of the solute diffusivity and the viscosity of the mobile phase together with the inverse of the fourth power of (or1) A graph relating (op) to the separation ratio of the critical pair is shown in figure (6)... 

The problem to be solved in this paragraph is to determine the rate of spread of the chromatogram under the following conditions. The gas and liquid phases flow in the annular space between two coaxial cylinders of radii ro and r2, the interface being a cylinder with the same axis and radius rx (0 r0 < r < r2). Both phases may be in motion with linear velocity a function of radial distance from the axis, r, and the solute diffuses in both phases with a diffusion coefficient which may also be a function of r. At equilibrium the concentration of solute in the liquid, c2, is a constant multiple of that in the gas, ci(c2 = acj) and at any instant the rate of transfer across the interface is proportional to the distance from equilibrium there, i.e. the value of (c2 - aci). The dispersion of the solute is due to three processes (i) the combined effect of diffusion and convection in the gas phase, (ii) the finite rate of transfer at the interface, (iii) the combined effect of diffusion and convection in the liquid phase. In what follows the equations will often be in sets of five, labelled (a),..., (e) the differential equations expression the three processes (i), (ii) (iii) above are always (b), (c) and (d), respectively equations (a) and (e) represent the condition that there is no flow over the boundaries at r = r0 and r = r2. 

We may compare this with the dispersion of a solute diffusing, with diffusion coefficient D, in a stream of velocity V. Here... 

Dialysis is particularly useful for removing small dissolved molecules from colloidal solutions or dispersions - e.g. extraneous electrolyte such as KNO3 from Agl sol. The process is hastened by stirring so as to maintain a high concentration gradient of diffusible molecules across the membrane and by renewing the outer liquid from time to time (Figure 1.5). 

The speed of a chromatographic separation is fixed by the particle size, the stationary phase characteristics, the available pressure, the solvent viscosity, the solute diffusivity, the a values of the critical pair, and extracolumn dispersion. One way to achieve faster separations is to reduce the particle size of the stationary phase. However, if material of smaller diameter is packed into a conventional size column, the backpressure will become prohibitively high. Thus, in a compromise between speed and optimum performance, narrow (<2 mm) columns packed with small 3-5 ju.m diameter particles have been developed. 

Diffusion, dispersion, and mass transfer are three ways to describe molecular mixing. Diffusion, the result of molecular motions, is the most fundemental, and leads to predictions of concentration as a function of position and time. Dispersion can follow the same mathematics used for diffusion, but it is due not to molecular motion but to flow. Mass transfer, the description of greatest value to the chemical industry, commonly involves solutes moving across interfaces, most commonly, fluid-fluid interfaces. Together, these three methods of analysis are important tools for chemical engineering. 

Denitrification, 340,473 Desorption, 221,362 Diffuse double layer, 141 Model, 142-146 Thickness, 145 Variable-charge surfaces, 146 Constant-charge surfaces, 143-146 Diffusion, 298, 398 Film diffusion, 398 Particle diffusion, 398 Solution diffusion, 398 Dioctahedral silicates, 122 Dispersion, 367... 

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