Transport fluxes

Pick s first law and equating the transport flux J with the rate / of an electrochemical reaction... 

The independent transport fluxes of simultaneous (coupled) heat- and mass-transfer in an n-component gas-liquid dispersion consisting of two phases (a = 1,2) can be written as (G3)... 

From Equation (34), the transport flux F,i, then becomes... 

Passive transport flux is therefore linearly dependent on mucosal solute concentration, provided the transported solute is readily removed by the villus blood supply (sink conditions). 

Once the value of cM(ro, t) (which for simplicity will be denoted as from now on) is known, any physical quantity of the system can be computed. In particular, the incoming diffusive (or mass transport) flux ... 

Equation (17) shows quite elegantly that the biouptake flux is governed by the two fundamental parameters a and b. A set of limiting values of J is easily derived by using that (1 — x)1 2 approaches (l jx) for x [Pg.156]

Bosma et al. [1] have proposed including the details of extracellular substrate transport in the calculation of whole-cell Michaelis-Menten kinetics. For the situation of a quasi-steady-state (i.e. when the transport flux and the rate of degradation of the substrate are equal) the consumption of substrate by a microorganism is represented as a function of the distant, and effectively unavailable, substrate concentration ca ... 

Among the trace metals, Hudson and Morel [7] postulated that Fe and Zn were closest to a diffusion-limited situation based upon measured cellular metal quotas and concentrations in marine systems (e.g. Zn would be diffusion limited for cells > 20 pm). Similarly, Hassler and Wilkinson [90] showed that for cells grown under conditions of Zn starvation, transport was diffusion limited for [Zn2+] < 10 12 mol dm. Fortin and Campbell [91] showed that, in the presence of chloride, the Ag transport flux to Chlamydomonas reinhardtii was close to a diffusion limitation at the lower Ag concentrations that were examined. Diffusion limitation of trace metals is most likely in systems where the concentrations are low and concentrations of competing metals are high, especially for essential metals that are taken up by passive diffusion across the membrane [8], The final point of essentiality could be especially important when transport systems are upregulated in response to lowmetal concentrations (see also Section 2.2 [90,92]). 

Six coupled governing equations listed in Table 1 are valid in all regions of a PEFC, and fluxes at an internal boundary between two adjacent regions are automatically continuous. Such a single-domain model is well suited for CFD implementation. In contrast, multidomain models, such as the one developed by Dutta et al., compute separate solutions for the anode and cathode subdomains, respectively, and then patch the two solutions through the water transport flux across the MEA interface. Numerically, this model is characterized as a solver-in-solver situation. 

How the Transport Flux Is Linked to the Charge-Transfer Flux The Flux-Equality Condition... 

The junction at which this current equality holds is the jr = 0, or OHP.) But the transport-current density is the charge transported per mole of ions (i.e., nF) times the transport flux(i.e., the number of moles of ions transported across 1 cm of a transit plane per second). If the electron acceptors are not charged species (ions), one can still state the equality of currents in terms of fluxes by expressing (7.172) in terms of moles per unit area and time arriving at, and being reacted in, the intaphase... 

The flux continuity or flux equality condition can be applied even when the current density i and the transport flux,/ are changing with time. One simply structures dr into small time intervals and says that the condition is valid within this infinitesimal time. 

For example, 8 = 0.05 cm yields the correct order of magnitude for the maximum current the limiting current, l cf. Eq. (7.206)], that a particular charge-transfer reaction can support. This maximum is determined by the maximum transport flux of reactants under diffusion control, in the steady state. 

When an electronation reaction is occurring at an interface, the equality of the charge-transfer flux and the transport flux requires that... 

In the limit of a vanishingly small time interval, this term represents the rate at which the extensive property N is transported convectively with the fluid motion across the control surfaces out of the control volume. Given that the fluid flow can be described by a vector field V, the convective transport flux across the area A of the control surface can be written as... 

Great activity has also been evidenced in microlithographically fabricated arrays of microelectrodes, which are typically formed in one plane on an insulating substrate [7,8,13,34-45] for experiments involving either an array of electrodes held at a common potential [37,40,42,43], or an array of noninteracting electrodes held at two or more different applied potentials [42,44], or an array of interdigitated electrodes held at two different potentials [13,34,36,38,39,45-47]. Arrays have significantly better analytical detection limits than continuous electrodes of the same overall dimensions, due to enhanced mass transport fluxes that arise from an increase in the spatial dimensionality of mass transport due to the alternation of electrode zones with pas-... 

Table 3.20 Selective phase transport of metal cations by calixarenes from basic aqueous solution. The data represent the rate of cation transport (flux) across the phase boundary in moles s 1 m2 x 10s.

If diffusion through the stagnant boundary layer determines the rate of transport through A for the system, then one can assume a constant, location-independent concentration cP in P. The partition equilibrium is assumed to be reached on the boundary area between P and L at x = 0 and consequently K = cP/cL(0). If one lets the thickness of the diffusion layer in L next to the surface of P be 1L and if L assumes a constant concentration of cL then one can assume a constant material transport flux through the boundary layer for short time intervals that follows Fick s first law and the contribution of the flux to time t is expressed according to Eq. (7-16) ... 

Early investigations of the dual-sorption model started from the assumption that only Henry s part of the sorbed gas contributed to the gas transport, whereas the Langmuir part would not contribute to it, due to immobilisation. Then the transport flux would be... 

If the system is closed, then the transport fluxes T and P," are zero and rf([A [B]) = 0, and the total mass of reactants in state A plus reactants in state B in the system remains constant. 

Thermodynamic equilibrium is a special-case steady state that is obtained by closed systems. Open systems with steady (constant) transport fluxes may approach stable steady states that are not equilibrium states. For example, a non-equilibrium steady state is achieved by the system ofEquations (3.15) when J1/ = —J = J = constant. As in the case of the closed system, = 0 and [A] + [B] = X0... 

The magnesium transport flux is denoted JtM. Similarly, for potassium we have... 

Thus the exchange is electroneutral and not dependent on the membrane potential. Assuming that the species HPO/- is cotransported with H+ ion and that the transport flux does not saturate in H+ concentration, we have from Equation (7.9) the equation for flux ... 

Figure 9.2 Stoichiometric matrix for model of Varma and Palsson [204], Enzyme abbreviations, corresponding to reactions illustrated in Figure 9.1, are indicated for each column, corresponding to a reaction. Metabolite abbreviations for metabolite associated with rows of the matrix are indicated as well. VC02 is a transport flux, transporting CO2 out of the system. Other transport fluxes are not included here.

Analogous to the question of maximal ATP production, we can use linear programming to compute the maximum possible production of other cofactors. For example, this reaction network may be used in the cell to generate NADPH to be used in other metabolic pathways. To compute the maximal NADPH yield, we have to add a transport flux for NADPH to by adding a new column with non-zero entry 59,43 = — 1. 

The dashed line encloses the internal reactions, labeled J through 75 the processes J, Ji, and J% are transport fluxes that transport material into or out of the... 

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