Rate processes spatial diffusion

As active transport uses a carrier system, it is normally specific for a particular substance or group of substances. Thus, the chemical structure of the compound and possibly even the spatial orientation are important. This type of transport is normally reserved for endogenous molecules such as amino acids, required nutrients, precursors, or analogues. For example, the anticancer drug 5-fluorouracil (Fig. 3.6), an analogue of uracil, is carried by the pyrimidine transport system. The toxic metal lead is actively absorbed from the gut via the calcium transport system. Active uptake of the toxic herbicide paraquat into the lung is a crucial part of its toxicity to that organ (see chap. 7). Polar and nonionized molecules as well as lipophilic molecules may be transported. As active transport may be saturated, it is a zero-order rate process in contrast to passive diffusion (Fig. 3.3). 

Most of the models assume that neutral-species transport can be represented with either a well-mixed model or a plug flow model. The major drawback to these assumptions is that important inelastic rate processes such as molecular dissociation are usually localized in space in the reactor and are often fast compared with rates of diffusion or convection. As a result, the spatial variation of fluid flow in the reactor must be accounted for. This variation introduces a major complication in the model, because the solution of the nonisothermal Navier-Stokes equations in multidimensional geometries is expensive and difficult. 

Lombardo and Bell (1991) reviewed stochastic models of the description of rate processes on the catalyst surface, such as adsorption, diffusion, desorption, and surface reaction, which make it possible to account for surface structure of crystallites, spatial inhomogeneities, and local fluctuations of concentrations. Comparison of dynamic MC and mean-field (effective) description of the problem of diffusion and reaction in zeolites has been made by Coppens et al. (1999). Gracia and Wolf (2004) present results of recent MC simulations of CO oxidation on Pt-supported catalysts. 

Here T1U is the so called one-dimensional TST estimate for the rate and is mainly determined by the one-dimensional potential of mean force w(q). The depopulation factor Y becomes much smaller than unity in the underdamped limit and is important when the rate is limited by the energy diffusion process. In the spatial-diffusion-limited regime, the depopulation factor Y is unity but the spatial diffusion factor becomes much smaller than unity. The major theme of this review is theoretical methods for estimating the depopulation and spatial diffusion factors. 

If the potential w(q) is a purely parabolic barrier potential, then the associated GLE may be solved analytically by a normal mode transformation. The parabolic barrier approximation plays a central role in the theory of activated rate processes and is discussed in some detail in Sec. III. The parabolic barrier approximation leads to the concept of optimized planar dividing surfaces (32, 42). Section IV is devoted to the variational TST method and its application to STGLE s using optimized planar dividing surfaces. The applicability of the variational TST method to the general case, in which the bath is also anharmonic is reviewed in Sec. V. Sections III-V summarize the main ingredients necessary for a theory for the spatial diffusion factor k. ... 

The kinetic motion of molecules may cause them to change their spatial distribution through successive random movements. This is the process of diffusion, which is a transport property. Other transport properties include viscosity, electrical conductivity, and thermal conductivity. While diffusion is concerned with the transport of matter, these are associated with the transport of momentum, electrical charge, and heat energy, respectively. Transport is driven in each case by a gradient in the respective property. Thus, the diffusion rate of species A is given by Pick s law. 

Bacterial bio films. Bacterial biofilms are complex, 3-D communities found nearly everywhere in nature and are also associated with many human diseases. Detailed metabolic information is critical to understand and exploit beneficial biofilms as well as combat anti biotic-resistant, disease-associated forms. Biofilm imaging, transport and metabolite measurement methods and their correlation for live, non-invasive monitoring of biofilm processes were correlatively applied. NMR methods provide macroscopic structure, metabolic pathway and rate data, spatially resolved metabolite concentrations and water diffusion profiles within the biofilm. In particular, current depth-resolved spectroscopy methods are appUed to detect metabolites in 140-190 nl volumes within biofilms. The entire 3-D biofilm structure was imaged using MRI. This was then correlated to a fluorescent CLSM image. 

Figure 3.6. Spatial variation of the electrochemical potential, jl02-, of O2 in YSZ and on a metal electrode surface under conditions of spillover (broken lines A and B) and when equilibrium has been established. In case (A) surface diffusion on the metal surface is rate limiting while in case (B) the backspillover process is controlled by the rate, I/nF, of generation of the backspillover species at the three-phase-boundaries. This is the case most frequently encountered in electrochemical promotion (NEMCA) experiments as shown in Chapter 4.

---