Migration, equilibrium-controlled

If, as shown in Figure 5.13, hyperconjugation results in the formation of species possessing both double-bond character and associated hydrogen ions, equilibrium-controlled migration of the associated hydrogen ion can be expected. This transformation, shown in Scheme 5.8, is known as a 1,2-hydride shift and results in the migration of a proton from carbon 1 to carbon 2. 

Where dissolution or precipitation is sufficiently rapid, the species concentration quickly approaches the equilibrium value as water migrates along the aquifer the system is said to be reaction controlled. Alternatively, given rapid enough flow, water passes along the aquifer too quickly for the species concentration to be affected significantly by chemical reaction. The system in this case is transport controlled. The relative importance of reaction and transport is described formally by the nondimensional Damkohler number, written Da. 

When the amount of the sample is comparable to the adsorption capacity of the zone of the column the migrating molecules occupy, the analyte molecules compete for adsorption on the surface of the stationary phase. The molecules disturb the adsorption of other molecules, and that phenomenon is normally taken into account by nonlinear adsorption isotherms. The nonlinear adsorption isotherm arises from the fact that the equilibrium concentrations of the solute molecules in the stationary and the mobile phases are not directly proportional. The stationary phase has a finite adsorption capacity lateral interactions may arise between molecules in the adsorbed layer, and those lead to nonlinear isotherms. If we work in the concentration range where the isotherms are nonlinear, we arrive to the field of nonlinear chromatography where thermodynamics controls the peak shapes. The retention time, selectivity, plate number, peak width, and peak shape are no longer constant but depend on the sample size and several other factors. 

Vertical separator. Fig. 2 is a schematic of a vertical separator. In this configuration inlet flow enters the vessel through the side. As in the horizontal separator, the inlet diverter does the initial gross separation. Liquid flows down to the liquid collection section of the vessel, then down to the liquid outlet. As liquid reaches equilibrium, gas bubbles flow counter to the direction of liquid flow and eventually migrate to the vapor space. The level controller and liquid dump valve operate in the same manner as in a horizontal separator. 

Another important characteristic of the surface processes is a ratio g of the adspecies migration rate constant to those of the surface reaction, adsorption, and desorption rates. At small coverages the parameter g controls the surface process conditions r 1 in the kinetic and g l in the diffusion mode. A fast surface mobility of the adspecies and their equilibrium distribution on the surface are the most frequently adopted assumptions. At r < 1 the macroscopic concentrations of adspecies 6 cannot be used for calculating the process rates, and a more detailed description of their distribution is essential. 

Bidoglio, G., and Avogadro, A. (1989) Equilibrium and Kinetic Controls on the Subsurface Migration of Radioactive Contaminants, Geoderma 44, 203-209. 

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