Gradient transport hypothesis

For LES performed in physical space, the basic sub-grid stress model is the eddy-viscosity model proposed by Smagorinsky . The Smagorinsky model is based on the gradient transport hypothesis and the sub-grid viscosity concept, just as the Reynolds stress models based on the Boussinesq eddy viscosity hypothesis, and expressed as ... 

The structures are often of large scale, for example, of the same order as that of the mean flow. They have been found to be responsible for mechanisms that relate to the transport and the production in almost all commonly observed turbulent flows. Findings show the existence of the underlying orderliness in the apparent chaos of turbulent flows and have fostered many modifications to the traditional thinking of turbulence, such as the turbulent gradient transport hypothesis. Weakly nonlinear analysis has been shown to reproduce the large-scale phenomena in simple flows. 

The modeled transport equations for z differ mainly in the diffusion and secondary source term. Launder and Spalding (1972) and Chambers and Wilcox (1977) discuss the differences and similarities in more detail. The variable, z = e is generally preferred since it does not require a secondary source, and a simple gradient diffusion hypothesis is fairly good for the diffusion (Launder and Spalding, 1974 Rodi, 1984). The turbulent Prandtl number for s has a reasonable value of 1.3, which fits the experimental data for the spread of various quantities at locations far from the walls, without modification of any constants. Because of these factors, the k-s model of turbulence has been the most extensively studied and used and is recommended as a baseline model for typical internal flows encountered by reactor engineers. 

When Mitchell first described his chemiosmotic hypothesis in 1961, little evidence existed to support it, and it was met with considerable skepticism by the scientific community. Eventually, however, considerable evidence accumulated to support this model. It is now clear that the electron transport chain generates a proton gradient, and careful measurements have shown that ATP is synthesized when a pH gradient is applied to mitochondria that cannot carry out electron transport. Even more relevant is a simple but crucial experiment reported in 1974 by Efraim Racker and Walther Stoeckenius, which provided specific confirmation of the Mitchell hypothesis. In this experiment, the bovine mitochondrial ATP synthasereconstituted in simple lipid vesicles with bac-teriorhodopsin, a light-driven proton pump from Halobaeterium halobium. As shown in Eigure 21.28, upon illumination, bacteriorhodopsin pumped protons... 

For weak acids, e.g., salicylic acid, the dependency on a pH gradient becomes complex since both the passive diffusion and the active transport process will be dependent on the proton concentration in the apical solution [61, 63, 98, 105] and a lowering of the pH from 7.4 to 6.5 will increase the apical to basolateral transport more than 20-fold. Similarly, for weak bases such as alfentanil or cimetidine, a lowering of the pH to 6.5 will decrease the passive transport towards the basolateral side [105]. The transport of the ionizable compound will, due to the pH partition hypothesis, follow the pKa curve. 

In Illustrative Example 19.2 we discussed the flux of trichloroethene (TCE) from a contaminated aquifer through the unsaturated zone into the atmosphere. The example was based on a real case of a polluted aquifer in New Jersey (Smith et al., 1996). These authors compared the diffusive fluxes, calculated from measured TCE vapor concentration gradients, with total fluxes measured with a vertical flux chamber. They found that the measured fluxes were often several orders of magnitude larger than the fluxes calculated from Fick s first law. In these situations the vapor profiles across the unsaturated zone were not always linear. The authors attributed this to the influence of advective transport through the unsaturated zone. In order to test this hypothesis you are asked to make the following checks ... 

The chemiosmotic hypothesis had the great virtue of predicting the following consequences which could be tested (1) electron-transport driven proton pumps with defined stoichiometries and (2) a separate ATP synthase, which could be driven by a pH gradient or membrane potential. Mitchell s hypothesis was initially greeted with skepticism but it encouraged many people, including Mitchell and his associate Jennifer Moyle, to test these predictions, which were soon found to be correct.178... 

Crane, R.K. (1975). The gradient hypothesis and other models of carrier-mediated active transport. Rev. Physiol. Biochem. Pharmacol. 78, 101-149. 

Oxidative phosphorylation is ATP synthesis linked to the oxidation of NADH and FADH2 by electron transport through the respiratory chain. This occurs via a mechanism originally proposed as the chemiosmotic hypothesis. Energy liberated by electron transport is used to pump H+ ions out of the mitochondrion to create an electrochemical proton (H+) gradient. The protons flow back into the mitochondrion through the ATP synthase located in the inner mitochondrial membrane, and this drives ATP synthesis. Approximately three ATP molecules are synthesized per NADH oxidized and approximately two ATPs are synthesized per FADH2 oxidized. 

Oxidative phosphorylation is the name given to the synthesis of ATP (phosphorylation) that occurs when NADH and FADH2 are oxidized (hence oxidative) by electron transport through the respiratory chain. Unlike substrate level phosphorylation (see Topics J3 and LI), it does not involve phosphorylated chemical intermediates. Rather, a very different mechanism was proposed by Peter Mitchell in 1961, the chemiosmotic hypothesis. This proposes that energy liberated by electron transport is used to create a proton gradient across the mitochondrial inner membrane and that it is this that is used to drive ATP synthesis. Thus the proton gradient couples electron transport and ATP synthesis, not a chemical intermediate. The evidence is overwhelming that this is indeed the way that oxidative phosphorylation works. The actual synthesis of ATP is carried out by an enzyme called ATP synthase located in the inner mitochondrial membrane (Fig. 3). 

Vidaver, G.A. (1964b). Some tests for the hypothesis that the sodium ion gradient furnishes the energy for glycine- active transport by pigeon red cells. Biochemistry 3, 803-808. 

Figure 17.2 The chemiosmotic hypothesis. Electrons from NADH and/or FADH2 are passed to Oz via the electron transport chain. In the process, protons are extruded into the mitochondrial intermembrane space. The proton gradient thus created causes the movement of protons back into mitochondria through a channel in the F ATPase. In the process, one molecule of ATP is formed frm ADP and phosphate for every two to three protons channeled back into the mitochondria. ATP moves into the intermembrane space and cytosol in exchange for ADP moving in the opposite direction. Phosphate is taken up in exchange for OH".

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