Coherent transport process

In addition to measurements of how much and what type of chemical species are present, modification of the MR experiment allows us to identify the physical state of a given species (e.g., gas, liquid, gel, and solid) and to quantify temperature and any incoherent and/or coherent transport processes within the system. By integrating any of these measurements into an imaging experiment, we can spatially map these quantities or exploit the effect of these characteristics on the magnitude or frequency of the MR signal to preferentially observe sub-populations of spins within the system. In this latter application we are exploiting the so-called contrast mechanisms in the image acquisition. These concepts are illustrated in Sections II.B II.D. 

From this descriptive introduction, it follows that the coherent spinodal decomposition is a continuous transport process occurring in a supersaturated matrix. It is driven by chemical potential gradients. Strain energy and concentration gradient energy have to be adequately included in the component chemical potentials. We expect that the initial stages of decomposition are easier to treat quantitatively than the later ones. The basic result will be the (directional) build-up of periodic variations in concentration [J.W. Cahn (1959), (1961), (1968)]. 

This volume aims at providing a coherent presentation of recent developments and understanding of heavy metal reactivity in soils. Such an understanding is necessary in addressing heavy metals concerns in the environment. The implicit framework of multiple reactivity acknowledges the widely known role played by the various colloidal surface functional groups in concomitant reactions. This overarching frame of reference allows unification between molecular structure-reactivity relationships at one scale and transport processes at the other. 

The transport mechanism—coherent versus incoherent—can have a strong influence on the overall probability that a photon absorbed somewhere in the antenna will feed the reaction center with energy. Suppose the transfer is stochastic and occurs with a probability p per individual step. If there are n transfer steps, the overall probability that energy is fed into the reaction center is p" and can be rather low although p may be close to 1. On the other hand, if transport is coherent, the process of feeding the reaction center can be viewed as kind of an internal conversion process in a supermolecule comprising the various chromophores. As... 

Fluid motion for Re = 1-100 indicates that the flow is laminar and transmission is characterized by laminar-advective transport. A low flow velocity or small length scale also means that molecular diffusion can be an important transport process relative to advective transport (i.e., Pe is low). Flow streamlines in low Re environments do not cross and the odor plume or trail consequently is relatively coherent and characterized by sharp gradients in chemical concentration, particularly in the axial (cross-flow) direction. This regime is important for smaller animals, particularly those in the plankton. Cruising copepods typically have a Re < 10, for instance, and the wake retains high concentration of scent in an isolated region due to the slow diffusive spread and dilution in the laminar regime (Yen et al. 1998). 

The above questions may be addressed at various levels of complexity and certainty depending on the size and complexity of the site under consideration. The material presented in this chapter is intended to serve the full range of user needs. This range of users includes those seeking a single value numerical estimate of the deposition and resuspension kinetic parameters, often used in trying to understand the relative importance of particle and associated contaminant transport compared to other contaminant fate and transport processes active at a specific site. In other words, they are trying to build a conceptual site model but are limited as to a complete and coherent data... 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

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