Diffusive mixing microscopic

Transport Chemicals are moved or transported by advection - moving water carries the dissolved solids with it - and hydrodynamic dispersion - the spreading and mixing caused in part by molecular diffusion and microscopic variation in velocities within individual pores (Mercer and Faust, 1981). 

Fig. 6.12. Determination of diffusion coefficients of deuterated PE s in a PE matrix by infrared absorption measurements in a microscope. Concentration profiles obtained in the separated state at the begin of a diffusion run and at a later stage of diffusive mixing (the dashed lines were calculated for monodisperse components the deviations are due to polydispersity) (left). Diffusion coefficients at T = 176°C, derived from measurements on a series of d-PE s of different molecular weight (right). The continuous line corresponds to a power law D M. Work of Klein [68]...

Mixing of fluid elements having different ages. Microscopic mixing produced by eddy diffusion effects is an example of this case. 

The limiting reaction rate achieved by diffusion occurring after mixing solutions containing two or more reactants. This form of control, also called mixing control, is typically more relevant for reactions involving heterogeneous systems (e.g., solid/liquid or liquid/gas). See also Microscopic Diffusion Control... 

One of the most important processes involved in the scale-up of liquid parenteral preparations is mixing [1]. For liquids, mixing can be defined as a transport process that occurs simultaneously in three different scales, during which one substance (solute) achieves a uniform concentration in another substance (solvent). On a large, visible scale, mixing occurs by bulk diffusion, in which the elements are blended by the pumping action of the mixer s impeller. On the microscopic scale, elements that are in proximity are blended by eddy currents, and they 43... 

The term macroscopic diffusion control has been used to describe processes in which the rate of reaction is determined essentially by the rate of mixing of the reactant solutions. The nitration of toluene in sulpholane by the addition of a solution of nitronium fluoroborate in sulpholane appears to fall into this class (Ridd, 1971a). Obviously, if a reaction is subject to microscopic diffusion control when the reactants meet in a homogeneous solution, it must also be subject to macroscopic diffusion control when preformed solutions of the same reactants are mixed. However, the converse is not true. The difficulty of obtaining complete mixing of solutions in very short time intervals implies that a reaction may still be subject to macroscopic diffusion control when the rate coefficient is considerably below that for reaction on encounter. The mathematical treatment and macroscopic diffusion control has been discussed by Rys (Ott and Rys, 1975 Rys, 1976), and has been further developed recently (Rys, 1977 Nabholtz et al, 1977 Nabholtz and Rys, 1977 Bourne et al., 1977). It will not be considered further in this chapter. 

The study of oxygen diffusion in oxides with mixed-valence 3d-ions presents great interest both in theoretical and practical terms. Such systems with Jahn-Teller (JT) 3d-cations are suitable model objects for analysis of the diffusion process in degenerate or pseudo-degenerate condensed systems. The mechanism of multi-well potential formation has been explored well for JT ions [1,2] and it is possible to give a simple microscopic description of the inter-center interactions and different properties of these systems. The practical interest paid to diffusion properties of the... 

Apparent rate laws include both chemical kinetics and transport-controlled processes. One can ascertain rate laws and rate constants using the previous techniques. However, one does not need to prove that only elementary reactions are being studied (Skopp, 1986). Apparent rate laws indicate that diffusion or other microscopic transport phenomena affect the rate law (Fokin and Chistova, 1967). Soil structure, stirring, mixing, and flow rate all affect the kinetic behavior when apparent rate laws are operational. 

They measured the zero potential point of the system, which depends on the halide concentration and type as described by the equations above. They were able to measure the effect of diffusion of species to the electrode and were able to determine a mixed potential of the electrode where the forward transfer of electrons from the silver was equal to the rate of reduction of the oxidant. This is shown diagram-matically in Figure 31. Nickel et al. found that the adsorption of halide to the silver surface did not influence the potential if the halide layer was less than 5 pm thick, but they did note that at a clean silver surface the silver halide formation began at a higher potential than expected, which they attributed to the high solubility of microscopic silver on the surface. 

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