Mass transport difference

Taking account chemical reaction and mass transport differences between elements, then we can infer the distribution of secondary minerals by considering thermodynamic constraints, as well as kinetic and transport phenomena. Solubility (Shikazono, 1988) and mass transport coefficient of Ca is large at low temperature, and therefore Ca is readily dissolved in shallow zones and transported to deeper levels. As a result, Ca-bearing alteration minerals, such as Ca-montmorillonite, occur widely in a geothermal field. Solubility and mass transport coefficient of Ca decreases with increasing temperature, so Ca-zeolites precipitate in the active zones. 

A number of different types of experiment can be designed, in which disc and ring can either be swept to investigate the potential region at which the electron transfer reactions occur, or held at constant potential (under mass-transport control), depending on the infomiation sought. 

A microelectrode is an electrode with at least one dimension small enough that its properties are a fimction of size, typically with at least one dimension smaller than 50 pm [28, 29, 30, 31, 32 and 33]. If compared with electrodes employed in industrial-scale electrosynthesis or in laboratory-scale synthesis, where the characteristic dimensions can be of the order of metres and centimetres, respectively, or electrodes for voltannnetry with millimetre dimension, it is clear that the size of the electrodes can vary dramatically. This enonnous difference in size gives microelectrodes their unique properties of increased rate of mass transport, faster response and decreased reliance on the presence of a conducting medium. Over the past 15 years, microelectrodes have made a tremendous impact in electrochemistry. They have, for example, been used to improve the sensitivity of ASV in enviroiunental analysis, to investigate rapid... 

Of course, in order to vary the mass transport of the reactant to the electrode surface, the radius of the electrode must be varied, and this unplies the need for microelectrodes of different sizes. Spherical electrodes are difficult to constnict, and therefore other geometries are ohen employed. Microdiscs are conunonly used in the laboratory, as diey are easily constnicted by sealing very fine wires into glass epoxy resins, cutting... 

Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

The shape of a voltammogram is determined by several experimental factors, the most important of which are how the current is measured and whether convection is included as a means of mass transport. Despite an abundance of different voltam-metric techniques, several of which are discussed in this chapter, only three shapes are common for voltammograms (figure 11.33). 

In the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

When two reactants in a catalytic process have such different solubiUty properties that they can hardly both be present in a single Hquid phase, the reaction is confined to a Hquid—Hquid interface and is usually slow. However, the rate can be increased by orders of magnitude by appHcation of a phase-transfer catalyst (40,41), and these are used on a large scale in industrial processing (see Catalysts, phase-TRANSFEr). Phase-transfer catalysts function by faciHtating mass transport of reactants between the Hquid phases. Often most of the reaction takes place close to the interface. 

Fig. 1. General dialysis is a process by which dissolved solutes move through a membrane in response to a difference in concentration and in the absence of differences in pressure, temperature, and electrical potential. The rate of mass transport or solute flux, ( ), is directly proportional to the difference in concentration at the membrane surfaces (eq. 1). Boundary layer effects, the difference between local and wall concentrations, are important in most...

Equation (22-66) assumes that all mass transport is caused by an electrical potential difference ac ting only on cations and anions. Assuming the transfer of electrical charges is due to the transfer of... 

In the classical set-up of bulk liquid membranes, the membrane phase is a well-mixed bulk phase instead of an immobilized phase within a pore or film. The principle comprises enantioselective extraction from the feed phase to the carrier phase, and subsequently the carrier releases the enantiomer into the receiving phase. As formation and dissociation of the chiral complex occur at different locations, suitable conditions for absorption and desorption can be established. In order to allow for effective mass transport between the different liquid phases involved, hollow fiber... 

If a diffusion potential occurs inside the membrane, the relation between mass transport and electrochemical potential gradient — as the driving force for the diffusion of ions — has to be examined in more detail. This can be done by three different approaches ... 

The rate of extraction depends on the mass transport coefficient (f), the phase contact area (F) and the difference between the equilibrium concentration and the initial concentration of the dissolved component, which is usually expressed as the driving force of the process (a). The rate of extraction (V) can be calculated as shown in Equation (135) ... 

Mass transport occurs by three different modes ... 

In this section we consider experiments in which the current is controlled by the rate of electron transfer (i.e., reactions with sufficiently fast mass transport). The current-potential relationship for such reactions is different from those discussed (above) for mass transport-controlled reactions. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Continuous CO Oxidation on Piatinum The main difference between CO stripping and continuous CO oxidation is the CO (re-)adsorption Reaction (6.3). In contrast to CO stripping, this leads a steady-state CO oxidation current because of the continuous supply of CO. In modeling the continuous CO oxidation, we also need to consider the mass transport of CO from the bulk of the solution to the electrode surface. The temporal change in the CO coverage is now given by... 

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