Homogeneous linear driving force

The solubilization and aqueous-phase transport of a NAPL in a homogeneous soil column can be represented using a one-dimensional form of the advective-dispersive reactive (ADR) transport equation. Employing a linear driving force expression to describe NAPL dissolution into the aqueous phase, the 1-D ADR equation may be written as ... 

Many homogeneous reactions occur in the liquid phase, but consume reactants that must be supplied by mass transfer from a gas phase (or occasionally from another liquid phase). This is a typical problem of reaction engineering and is treated in some detail in most modem texts of that field [1,3,4,9,16,17]. Customarily, a power law is assumed for the rate of the chemical reaction and is then combined with a standard linear-driving force or Fickian diffusion treatment of mass transfer. A mass-transfer limitation lowers the rate, which in some extreme situations can become entirely mass transfer-controlled. Certain types of multistep reactions, however, can produce a totally different and very interesting behavior that may involve instability. 

The breakthrough curve for solid homogeneous diffusion (linear driving force) combined with film mass transfer can be derived ... 

It seems clear that for reactions of carbocations with nucleophiles or bases in which the structure of the carbocation is varied, we can expect compensating changes in intrinsic barrier and thermodynamic driving force to lead to relationships between rate and equilibrium constants which have the form of extended linear plots of log k against log K. However, this will be strictly true only for structurally homogeneous groups of cations. There is ample evidence that for wider structural variations, for example, between benzyl, benzhydryl, and trityl cations, there are variations in intrinsic barrier particularly reflecting steric effects which lead to dispersion between families of cations. 

The Soret effect is effectively a liquid junction potential produced by a temperature gradient in a homogeneous electrolyte. The activity coefiicients of ions are generally not identical consequently, a temperature gradient produces a driving force, which will be opposed by potential. The implications of the Soret effect in an ILIT perturbation were discussed by Smalley et al. [5], who showed that there is a linear relationship between the Soret potential, A Fsoret, and the temperature difference between the electrode surface and the bulk solution, AT, i.e. ... 

An extended Stefan-Maxwell diffusion equation can be constructed by setting up a homogeneous, linear relationship between the vector of diffusion driving forces and the vector of species velocity differences. 

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