Diffusive spreading coefficient

In the group with negative spreading coefficients (e.g., kerosene-in-water and paraffin-in-water emulsions), the values of kLa in both stirred tanks and bubble columns decrease linearly with an increasing oil fraction. This effect is most likely due to the formation of lens-like oil droplets over the gas-liquid interface. A subsequent slower oxygen diffusion through the droplets, and/or slower rates of surface renewal at the gas-liquid surface, may result in a decrease in kLa. 

Many studies are available dealing with radial spreading from single points or other geometries (Hoftyzer, I96U Onda et al., 1973 Herskowitz et al., 1979). In these studies, the liquid spreading is supposed to be ruled by some diffusional mechanism, which leads to write a diffusion-like equation introducing a radial spread coefficient Dp ... 

The spreading rate of a polymer droplet on a surface has been measured (363,364). The diffusion constant was at least an order of magnitude smaller than that of the bulk. The monomer—surface friction coefficient for polystyrene has been measured on a number of surfaces and excellent... 

Dispersion Model An impulse input to a stream flowing through a vessel may spread axially because of a combination of molecular diffusion and eddy currents that together are called dispersion. Mathematically, the process can be represented by Fick s equation with a dispersion coefficient replacing the diffusion coefficient. The dispersion coefficient is associated with a linear dimension L and a linear velocity in the Peclet number, Pe = uL/D. In plug flow, = 0 and Pe oq and in a CSTR, oa and Pe = 0. 

The distribution of tracer molecule residence times in the reactor is the result of molecular diffusion and turbulent mixing if tlie Reynolds number exceeds a critical value. Additionally, a non-uniform velocity profile causes different portions of the tracer to move at different rates, and this results in a spreading of the measured response at the reactor outlet. The dispersion coefficient D (m /sec) represents this result in the tracer cloud. Therefore, a large D indicates a rapid spreading of the tracer curve, a small D indicates slow spreading, and D = 0 means no spreading (hence, plug flow). 

With the Laplace operator V. The diffusion coefficient defined in Eq. (62) has the dimension [cm /s]. (For correct derivation of the Fokker-Planck equation see [89].) If atoms are initially placed at one side of the box, they spread as ( x ) t, which follows from (62) or from (63). 

The translational diffusion coefficient in Eq. 11 can in principle be measured from boimdary spreading as manifested for example in the width of the g (s) profiles although for monodisperse proteins this works well, for polysaccharides interpretation is seriously complicated by broadening through polydispersity. Instead special cells can be used which allow for the formation of an artificial boundary whose diffusion can be recorded with time at low speed ( 3000 rev/min). This procedure has been successfully employed for example in a recent study on heparin fractions [5]. Dynamic fight scattering has been used as a popular alternative, and a good demonstra-... 

In ultra-thin films, on the other hand, the mechanism of spreading is dominated by surface diffusion so that the diffusion coefficients can be written as... 

More recently, three-dimensional (3D) pulse sequences with DOSY have been presented where a diffusion coordinate is added to the conventional 2D map. As in the conventional 2D spectra, these experiments reduce the probability of signal overlap by spreading the NMR frequency of the same species over a 2D plane, and distribute the diffusion coefficient. 

We now make two simplifications. One is that the rate of O2 production is uniform over the curved part of the Pt surface, and we ignore the contribution from the end of the rod because it is small in surface area when compared to the rest of the rod. Second, the rod is permeable to O2, with the same diffusion coefficient as in water because the rod is small with respect to the diffusion length in the volume of the solution for the time scale of motion. With these approximations, the problem can be solved by integrating the contributions of a continuum of point sources spread on the cylindrical Pt surface (Eq. (3))... 

In population genetics there is experimental evidence that many mutations are neutral, which is consistent with Kimura s theory of neutral evolution [19]. Kimura s theory is based on a neutrality condition, that is, on the assumption that the natality and mortality functions as well as the transport (migration) coefficients are the same for the main population as well as for the mutants. For neutral mutations the nonlinear reaction-diffusion equations for the spreading of a mutation within a growing population which is expanding in space have a... 

Pollutants emitted by various sources entered an air parcel moving with the wind in the model proposed by Eschenroeder and Martinez. Finite-difference solutions to the species-mass-balance equations described the pollutant chemical kinetics and the upward spread through a series of vertical cells. The initial chemical mechanism consisted of 7 species participating in 13 reactions based on sm< -chamber observations. Atmospheric dispersion data from the literature were introduced to provide vertical-diffusion coefficients. Initial validity tests were conducted for a static air mass over central Los Angeles on October 23, 1968, and during an episode late in 1%8 while a special mobile laboratory was set up by Scott Research Laboratories. Curves were plotted to illustrate sensitivity to rate and emission values, and the feasibility of this prediction technique was demonstrated. Some problems of the future were ultimately identified by this work, and the method developed has been applied to several environmental impact studies (see, for example, Wayne et al. ). 

---