Transport kinetics, source

With the increased computational power of today s computers, more detailed simulations are possible. Thus, complex equations such as the Navier—Stokes equation can be solved in multiple dimensions, yielding accurate descriptions of such phenomena as heat and mass transfer and fluid and two-phase flow throughout the fuel cell. The type of models that do this analysis are based on a finite-element framework and are termed CFD models. CFD models are widely available through commercial packages, some of which include an electrochemistry module. As mentioned above, almost all of the CFD models are based on the Bernardi and Verbrugge model. That is to say that the incorporated electrochemical effects stem from their equations, such as their kinetic source terms in the catalyst layers and the use of Schlogl s equation for water transport in the membrane. 

EHC monographs examine the physical and chemical properties and analytical methods sources of environmental and industrial exposure and environmental transport kinetics and meta-bohsm including absorption, distribution, transformation, and elimination short- and long-term effects on animals, carcinogenicity, mutagenicity, and teratogenicity and finally, an evaluation of risks for human health and the effects on the environment. 

Carrier-mediated passage of a molecular entity across a membrane (or other barrier). Facilitated transport follows saturation kinetics ie, the rate of transport at elevated concentrations of the transportable substrate reaches a maximum that reflects the concentration of carriers/transporters. In this respect, the kinetics resemble the Michaelis-Menten behavior of enzyme-catalyzed reactions. Facilitated diffusion systems are often stereo-specific, and they are subject to competitive inhibition. Facilitated transport systems are also distinguished from active transport systems which work against a concentration barrier and require a source of free energy. Simple diffusion often occurs in parallel to facilitated diffusion, and one must correct facilitated transport for the basal rate. This is usually evident when a plot of transport rate versus substrate concentration reaches a limiting nonzero rate at saturating substrate While the term passive transport has been used synonymously with facilitated transport, others have suggested that this term may be confused with or mistaken for simple diffusion. See Membrane Transport Kinetics... 

The above quantities are accessible by standard measurements of liquid membrane transport and are frequently reported in the corresponding literature. To emphasize the kinetic source of separations studied, all computations have been carried out after assuming the same equilibrium constants for cation-exchange reactions appearing in the pertraction system, i.e.. 

For properly chosen conditions the epitaxial layer growth rate is limited only by the rate of vapour transport from source to substrate and it is hardly affected by surface phenomena kinetics [30-33]. Since the silicon vapour pressure sufficiently exceeds the pressures of carbon-containing species, the vapour flow from source to substrate is limited by the transport of carbon, and the flux qsiC is given by ... 

Multiscale models can be based only on continuum mathematical descriptions, e.g., as in the zeolite-based chemical reactor illustrated in Fig. 5, where the conservation equation describing the reactant transport along the reactor has a source term being calculated from the boundary condition of a macropore diffusion model with a source term calculated in turn from the boundary condition of a micropore diffusion model with a reaction kinetics source term [44]. 

Kozlowski et al. [18] obtained the p CD polymers, which were prepared by crosslinking of 3-CD with 2-(l-docosenyl)-succinic anhydride derivatives in anhydrous N,N-dimethylformamide in the presence of NaH. It was established that the elongation of the hydrocarbon chain in the obtained 3-CD polymer in the reaction with 2-(l-docosenyl)-succinic anhydride results in the selectivity for Pb(ll) ions in the ion transport with the use of this ion carrier. At room temperature the dimmer was obtained, while at 100°C the polymers of 34kD and 13.5 kD fractions were received. The transport kinetics investigation on dependence of the carrier and Pb(II) concentrations have shown that the transport by the dimmer proceeded by the facilitated mechanism, typical for liquid membranes. The polymer however, has shown a linear increase of the transport flux in dependence on metal concentration in the source phase, this fact indicating that the polymer form of 3-CD prefers probably the fixed site mechanism of transport. PIMs containing dimmer and polymer of CD, in the transport of Zn(II), Cu(II) and Pb(Il) showed selectivity orders Pb(Il) Cu(II), Zn([]), and Pb(II) Cu(II) > Zn(II), respectively. The high selectivity factor for Pb(II)/Cu(II) equal to 163 for the dimmer was achieved (Table 1). 

Selectivity in FIA is often better than that for conventional methods of analysis. In many cases this is due to the kinetic nature of the measurement process, in which potential interferents may react more slowly than the analyte. Contamination from external sources also is less of a problem since reagents are stored in closed reservoirs and are pumped through a system of transport tubing that, except for waste lines, is closed to the environment. 

The work of Verbrugge and Tobias on CdTe [8] comprises a comprehensive source of information about the electrochemistry of the compound and its components. Deposition features are reviewed, and thermodynamic, transport, and kinetic parameters for cadmium and tellurium deposition are reported. 

The transport equations for the turbulent kinetic energy, k, and the turbulence dissipation, e, in the RNG k-s model are again defined similar to the standard k-s model, now utilizing the effective viscosity defined through the RNG theory. The major difference in the RNG k-s model from the standard k-s model can be found in the e balance where a new source term appears, which is a function of both k and s. The new term in the RNG k- s model makes the turbulence in this model sensitive to the mean rate of strain. The result is a model that responds to the effect of strain and the effect of streamline curvature,... 

The mobilization of arsenic from the tailings material seems to be a slow and continuos process attributed to reduction of iron phases. The seepage water of the middle source contains arsenite as well as arsenate in high concentrations and seems to be the only water source in contact with the tailings material. The concentrations of arsenic downstream are still high and the immobilization process by precipitation of iron hydroxide and coprecipitation or sorption of arsenic is incomplete. A reason for this may be the slow kinetics of the oxidation process and the transport of fine grained hydroxide particles. These particles are mobile and can bind the arsenic (mainly as arsenate) too. 

In a transported PDF simulation, the chemical source term, (6.249), is integrated over and over again with each new set of initial conditions. For fixed inlet flow conditions, it is often the case that, for most of the time, the initial conditions that occur in a particular simulation occupy only a small sub-volume of composition space. This is especially true with fast chemical kinetics, where many of the reactions attain a quasi-steady state within the small time step At. Since solving the stiff ODE system is computationally expensive, this observation suggests that it would be more efficient first to solve the chemical source term for a set of representative initial conditions in composition space,156 and then to store the results in a pre-computed chemical lookup table. This operation can be described mathematically by a non-linear reaction map ... 

In cases where the depuration of HOCs from BMOs involves enzyme-mediated biotransformations (Eq. 7.4) or active transport mechanisms, and environmental concentrations are high (e.g. near a point source), depuration rates have been shown to follow Michaelis-Menten kinetics (Spade and Hamelink, 1985). Michaelis-Menten kinetics is elicited when an enzyme or active transport system is saturated with a chemical. This type of kinetics is characterized by lower values of keS at sites with high HOC concentrations. If k s are unchanged at high concentration sites, Michaelis-Menten kinetics will result in elevated BAFs. However, if chemical concentrations become toxic, finfish likely avoid the area and sessile organisms such as mussels may close their valves for extended periods (Huckins et al., 2004). 

Lifetime performance degradation is a key performance parameter in a fuel cell system, but the causes of this degradation are not fully understood. The sources of voltage decay are kinetic or activation loss, ohmic or resistive loss, loss of mass transport, or loss of reformate tolerance (17). 

J. Srmivason, et al., "High Energy Efficiency and High Power Density Proton Exchange Membrane Fuel Cells - Electrode Kinetics and Mass Transport," Journal of Power Sources, p. 36, 1991. 

The challenge for modeling the water balance in CCL is to link the composite, porous morphology properly with liquid water accumulation, transport phenomena, electrochemical kinetics, and performance. At the materials level, this task requires relations between composihon, porous structure, liquid water accumulation, and effective properhes. Relevant properties include proton conductivity, gas diffusivihes, liquid permeability, electrochemical source term, and vaporizahon source term. Discussions of functional relationships between effective properties and structure can be found in fhe liferafure. Because fhe liquid wafer saturation, 5,(2)/ is a spatially varying function at/o > 0, these effective properties also vary spatially in an operating cell, warranting a self-consistent solution for effective properties and performance. 

A fundamental fuel cell model consists of five principles of conservation mass, momentum, species, charge, and thermal energy. These transport equations are then coupled with electrochemical processes through source terms to describe reaction kinetics and electro-osmotic drag in the polymer electrolyte. Such convection—diffusion—source equations can be summarized in the following general form... 

---