Parallel-flow pathway

Figure 3. Conventional parallel-flow pathway (retentate flow only shown). Key 1, retentate inlet distribution manifold ...

The renal clearance of sulfamethoxazole, but not of its metabolite, Nij-acetylsulfamethoxazole, was markedly influenced by urinary pH and urine flow. Pharmacokinetic analysis of percutaneous absorption showed evidence of parallel penetration pathways for methotrexate when it was topically applied to hairless mouse skin. ... 

Oxidation of aqueous phenol solutions was studied over various catalysts in a semibatch slurry and continuous-flow fixed-bed reactors at temperatures up to 463 K and pressures slightly above atmospheric. The results show that due to a complex consecutive-parallel reaction pathway and a heterogeneous-homogeneous free-radical mechanism both kinetics and reaction selectivity are strongly dependent on the type of reactor used. Although the catalysts employed were found to be active in converting aqueous phenol solutions to nontoxic compounds, neither metal oxides nor zeolites were stable at the reaction conditions. 

Transients in the rate of ammonia synthesis have been observed when the flow is changed [418, 536, 686, 687], when the reaction mixture is changed from N2 + 3H2 to pure H2 or to pure N2 [536, 687, 688], and when the temperature is changed [686]. The behavior under transient operation has been taken as evidence for auto catalysis [686, 536, 689] or for the existence of parallel reaction pathways [682, 683]. By modelling the situation of a reactor under transient operation it has been concluded [690] that limited information can be derived from such experiments. 

This sum can be viewed also as the parallel combination of m pathways, each characterized by a different rate constant and a uniform distribution of flow in the input of these pathways. Then, the negative power function behavior can be attributed to the heterogeneity of the flow in the system. 

Figure 8.8 Integrated modeling of transport and metabolism. An axially distributed model of oxygen transport and metabolism [14], with parallel pathways used to simulate heterogeneity in path length and flow is used to simulate an experiment in which coronary flow is reduced and myoglobin saturation and concentrations of phosphate metabolites are measured. Data are from Zhang et al. [218],...

The leaf resistance is in series with that of the boundary layer, Thus the total resistance for the flow of water vapor from the site of evaporation to the turbulent air surrounding a leaf (r al) is 4- (see Fig. 8-5). We now must face the complication created by the two leaf surfaces representing parallel pathways for the diffusion of water vapor from the interior of a leaf to the surrounding turbulent air. We will represent the leaf resistance for the pathway through the upper (adaxial) surface by rj afu and that for the lower (abaxial) surface by r af. Each of these resistances is in series with that of an air boundary layer—and for the upper and the lower leaf surfaces, respectively. The parallel arrangement of the pathways through the upper and the lower surfaces of a leaf leads to the following total resistance for the diffusion of water vapor from a leaf ... 

Equation 8.13b indicates that each pathway in parallel increases the flow and hence increases the overall conductance, gpaiaiiei-... 

Equations 8.11, 8.12, 8.14, and 8.15 are admittedly cumbersome—they are presented mainly to show how the influences of individual parts of the transpiration pathway in series and in parallel can be handled for resistances and for conductances. Moreover, they illustrate an approach that can be used in analogous flow situations to evaluate the importance of various components in series or in parallel. 

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