Colloid distribution coefficient

Figure 3. Distribution coefficient (Ka) versus particle concentration for Th. Note that, for typical open-ocean particle concentrations, Th is about lO times more likely to adhere to a mass of particles than to remain in the same mass of water. This tendency to be found in the particulate phase decreases with particle concentration, probably due to the presence of a larger number of colloids which, because they pass through filters, appear to be in the dissolved phase (Honeyman et al. 1988). Grey squares are " Th data from Honeyman et al. (1988) gray triangles are " Th data from the continental shelf from McKee et al. (1986) and black circles are a compilation of open ocean °Th data from Henderson et al. (1999a).

Baskaran and Santschi (1993) examined " Th from six shallow Texas estuaries. They found dissolved residence times ranged from 0.08 to 4.9 days and the total residence time ranged from 0.9 and 7.8 days. They found the Th dissolved and total water column residence times were much shorter in the summer. This was attributed to the more energetic particle resuspension rates during the summer sampling. They also observed an inverse relation between distribution coefficients and particle concentrations, implying that kinetic factors control Th distribution. Baskaran et al. (1993) and Baskaran and Santschi (2002) showed that the residence time of colloidal and particulate " Th residence time in the coastal waters are considerably lower (1.4 days) than those in the surface waters in the shelf and open ocean (9.1 days) of the Western Arctic Ocean (Baskaran et al. 2003). Based on the mass concentrations of colloidal and particulate matter, it was concluded that only a small portion of the colloidal " Th actively participates in Arctic Th cycling (Baskaran et al. 2003). 

We will analyze the latter case and follow the argumentation given by Morel and Gschwend (1987). Distinguishing between particles (that are retained in filters or that are separated in centrifugation) and colloids (that are in the filtrate or supernatant) we can characterize an "observed" distribution coefficient. 

Now, because the water-borne radioactive element is predominantly associated with the colloids, we no longer have a need for the distribution coefficient. There will still be a partitioning because the major portion of the radioactive elements will still be adsorbed to the sediment. This is a separate equilibrium partitioning coefficient, requiring a new experiment on the clay sediments and the colloids present. The partitioning colloid-clay ratio would most likely be dependent on the surface areas of each present in the sediments. A separate size distribution analysis has resulted in a sediment-colloid surface area ratio of 99 1 for the sediment. This results in a colloid retardation coefficient oiRc = 100 rather than Ri = 4.2 x 10 or i 2 = 6 x 10. ... 

In rivers and streams heavy metals are distributed between the water, colloidal material, suspended matter, and the sedimented phases. The assessment of the mechanisms of deposition and remobilization of heavy metals into and from the sediment is one task for research on the behavior of metals in river systems [IRGOLIC and MARTELL, 1985]. It was hitherto, usual to calculate enrichment factors, for instance the geoaccumulation index for sediments [MULLER, 1979 1981], to compare the properties of elements. Distribution coefficients of the metal in water and in sediment fractions were calculated for some rivers to find general aspects of the enrichment behavior of metals [FOR-STNER and MULLER, 1974]. In-situ analyses or laboratory experiments with natural material in combination with speciation techniques are another means of investigation [LANDNER, 1987 CALMANO et al., 1992], Such experiments manifest univariate dependencies for the metals and other components, for instance between different metals and nitrilotriacetic acid [FORSTNER and SALOMONS, 1991], but the interactions in natural systems are often more complex. 

Ion exchange is normally defined by a distribution coefficient or by a selectivity coefficient more than by an equilibrium exchange constant (see below). These coefficients relate the amount of the exchanged ions that stay in the colloidal solid matrix to that in the aqueous phase. In this context, a simplified example of an ion exchange reaction (e.g., H+ for K+) is... 

If the analytically determined dissolved phase contains colloids, artifacts in distribution coefficients, such as a so-called particle concentration effect... 

The distribution coefficients of Pa(V) between nitric acid solutions and solvents containing TBP are less than those of uranium [C6], and are less than those of thorium except at high concentrations of HNO3 [H2]. In extraction measurements it is found that the fraction of Pa(V) that can be extracted decreases with time, due evidently to the slow polymerization of Pa(V) colloids. The more highly condensed forms caimot be depolymetized by acid treatment [K2]. 

Kaplan et al. [100] measured nuclide distribution coefficients for Pu, Am, Cm, and U in groundwater colloids. This study showed the extent to which each actinide was associated with groundwater colloids, a potential cause for the apparently enhanced transport of the contaminants. 

Figure 11.4 Selective precipitation (i.e. phase split) for aqueous solutions containing two proteins, lysozyme and haemoglobin at pH 7 and ammonium sulfate - the salting out effect Ions of the electrolyte dehydrate the hydrophilic colloid, i.e. remove water from the polymer, whereby a phase split occurs where two liquids co-exist One of these phases is very dilute in protein while the other is highly concentrated and precipitation can take place. The experimental data show that when the ionic strength of ammonium sulfate exceeds about 7.5 M excellent separation of the proteins is obtained. K is the distribution coefficient of a given protein in the two liquid phases. Reprinted from Prausnitz (1995), with permission from Elsevier...

Obviously, the theory outhned above can be applied to two- and three-dimensional systems. In the case of a two-dimensional system the Fourier transforms of the two-particle function coefficients are carried out by using an algorithm, developed by Lado [85], that preserves orthogonality. A monolayer of adsorbed colloidal particles, having a continuous distribution of diameters, has been investigated by Lado. Specific calculations have been carried out for the system with the Schulz distribution [86]... 

Routh and Russel [10] proposed a dimensionless Peclet number to gauge the balance between the two dominant processes controlling the uniformity of drying of a colloidal dispersion layer evaporation of solvent from the air interface, which serves to concentrate particles at the surface, and particle diffusion which serves to equilibrate the concentration across the depth of the layer. The Peclet number, Pe is defined for a film of initial thickness H with an evaporation rate E (units of velocity) as HE/D0, where D0 = kBT/6jT ir- the Stokes-Einstein diffusion coefficient for the particles in the colloid. Here, r is the particle radius, p is the viscosity of the continuous phase, T is the absolute temperature and kB is the Boltzmann constant. When Pe 1, evaporation dominates and particles concentrate near the surface and a skin forms, Figure 2.3.5, lower left. Conversely, when Pe l, diffusion dominates and a more uniform distribution of particles is expected, Figure 2.3.5, upper left. 

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