Sedimentation equilibrium with diffusion

Note that if the sediment surface were to consist of freshly sedimented particles with concentration Cssc = C°p, then the pore water in equilibrium with these particles would have the aqueous concentration C c = C p, and thus according to Eq. 23-24 the diffusive exchange flux Fsed difr would be zero. However, in most cases the sediment surface is not in equilibrium with the water column, because diagenetic processes change the physicochemical properties of the sediments and thus its solid-water distribution ratio, Kf, relative to. Furthermore, the sediment surface usually reflects a longer history of exposure to the chemical under consideration than the water column. Therefore, water and sediments would approach equilibrium only if the external loading to the lake has changed very slowly in the past. For manmade chemicals this is usually not the case. 

Figure 7.13 Theoretical down-core profiles of radon activity illustrating that 222Rn is typically not in (a) secular equilibrium with its parent 226Ra at the sediment-water and water-atmosphere interfaces because of inert characteristics and loss by (b) diffusion and (c) gas bubble ebullitive stripping from sediments to overlying waters and then to the atmosphere. (Modified from Martens and Chanton, 1989.)...

On the basis of monomer molecular weights (from sedimentation-equilibrium and sedimentation—diffusion studies, amino acid sequences and compositions), the a-lactalbumins, with one exception (rat a-lactalbumin, 140 residues, see Section VII,B), have a single chain of — 123 residues and values of —14,000. The mammalian lysozymes have 128-130 residues and values of —14,400, except echidna lysozyme, which has —125 residues. The c-type hen egg-white lysozymes have -127—131 residues, in contrast to the g type, which has —185 residues. 

MIRAGE2 Bulk equilibrium with RH based on Kohler theory. Hysteresis is treated Mechanistic, parameterized activation based on Kohler theory bulk CCN only Modal activation. Brownian diffusion, autoconversion, precip. rate independent of aerosols Calculated modal scaveng. coeff using a parameterization of the collective efficiency of aerosol particles by rain drops with size dependence Two-moment sedimentation for aerosols, nosedimentation for cloud droplets/ices... 

A summary of degrees of polymerization reported for hardwood xylans and the methods used for their determination, together with isolation procedures, yields, and viscosity data, is presented in Table V. The methods used include osmometry, light-scattering, sedimentation equilibrium, and sedimentation-diffusion (not listed). Recourse has also frequently been had to chemical methods for determining chain length. These methods are, however, far less reliable than physical techniques, and they will not be... 

Equations (V.7) and (V.l 1) reflect the increase in the sedimentation rate with increasing particle size, and the increase in the rate of diffusion with a decrease in particle size. Thus, one may expect that for particles of intermediate size the sedimentation and diffusion fluxes can balance each other, i.e.Jd +js = 0, which leads to an equilibrium between sedimentation and diffusion ... 

For disperse systems consisting of particles with radii less than 0.1 pm direct observation of the equilibrium between sedimentation and diffusion is difficult or even impossible, as the equilibrium is reached extremely slowly. 

An alternative method of using the ultracentrifuge to measure molecular weights is to allow the distribution of particles to reach equilibrium. As sedimentation occurs in the ultracentrifuge a concentration gradient is established, and this will cause the molecules to diffuse in the opposite direction. Eventually the system reaches a state of equilibrium at which the rate with which the solute is driven outwards by the centrifugal force just equals the rate with which it diffuses inwards under the influence of the concentration gradient. 

Radon With its half-life of 3.8 days, the readily soluble gas Rn is in secular equilibrium with its parent "Ra in the interior ocean. At the boundaries of the ocean, however, inputs from sediments and release to the atmosphere create concentration gradients carrying useful kinetic information. The distribution of excess Rn near the seafloor is used to quantify vertical diffusion (see above. Figure 8) and ground-water inputs the depletion of Rn in surface waters has been used to quantify the air-sea gas exchange rate. 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

Finally, we consider the behavior of a solute in a solution in the cell subjected to the centrifugal field. At a suitable angular velocity, the tendency of the solute to sediment toward the bottom of the cell is countered by its tendency to diffuse backward toward the meniscus, because the concentration increases with increasing r, as indicated in Figure 2. 2 b). At some time, a sedimentation equilibrium is attained. A typical equilibrium concentration distribution is depicted in Figure 2. 2 b). Our aim is to find a quantitative analytical expression for this curve. 

In this paper we have used the quantity (1 — vp0) in writing equations for sedimentation equilibrium experiments. Some workers prefer to use the density increment, 1000(dp/dc)Tfn, instead when dealing with solutions containing ionizing macromolecules. This procedure was first advocated by Vrij (44), and its advantages are discussed by Casassa and Eisenberg (39). Nichol and Ogston (13) have used the density increment in their analysis of mixed associations. The subscript p. means that all of the diffusible solutes are at constant chemical potential in the buffer... 

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