Fluxes pressure effect

Cumo et al. (1969) reported that the pressure effect on the bubble diameter is linear in a Freon-114 flow, as shown in Figure 5.43. They tested the two-phase Freon-114 flow in a vertical rectangular test section at a mass flux of 100 g/cm2 s (0.737 x 106 lb/ft2 hr). The average bubble diameters at various system pressures were obtained from high-speed photographic recordings. The effect of reduced pressure, p pci, on the average diameter of Freon bubbles is correlated as... 

The effect of local enthalpy at CHF is due primarily to the wall voidage, which impairs the critical flux, and secondarily to the bulk voidage, which affects the flow pattern. The coupled effects of local subcooling and flow velocity in a subcooled bubbly flow were first reported by Griff el and Bonilla (1965), neglecting the pressure effect ... 

For the forced convective region, only limited data are available on the effects of the different variables involved, since the existence of this region has only been recognized recently. As previously mentioned, the velocity required for the suppression of nucleate boiling increases with pressure further, an increase in pressure reduced the specific volume of the vapour and hence the linear velocity of the two phase mixture at a given quality will be reduced. Thus higher velocities and steam qualities would be required for the forced convective region to be entered at the same heat flux. The effect of diameter is, as far as can be seen from the work of previous experiments and from these experiments, that to be expected with convective heat transfer, namely, that the coefficient is proportional to the diameter or the equivalent diameter to the power —02. 

The chemical process gives the enthalpy of reaction, the flow rate, the reaction time, and the required reaction temperature. The first step in the sizing procedure is to calculate the required number of channels for the heat exchanger. Then the pass arrangement is selected in order to achieve the highest possible Reynolds number within an acceptable pressure drop. For example, if the total number of channels is fixed by the residence time channels in series will induce high velocities and high pressure drop channels in parallel will induce low velocities and low pressure drop. The second step is to estimate the heat transfer coefficient and to check that the heat flux can effectively be controlled by the secondary fluid (the lower heat transfer coefficient should be on the reaction side). 

Barometric pressure effects are the best documented. Bogoslovskaya et al. (1932) measured the Rn flux in a plot of ground before and after burial of uraniferous rock at a depth of 5 m, and related changes in soil-gas Rn to barometric pressure. Their results are summarised in Table 11-XV. Note the large variation even at a depth of 4 m between rising and falling barometric pressures when U ore is present. Unfortunately these authors did not report the fluctuations of Rn in the overburden prior to the burial of ore, but did report the mean Rn content stabilised at a depth of 2 m. The results by... 

Figure 8 shows the flux and conductivity and color rejections for a dynamic membrane at various recovery levels using mixtures of the range wash water effluents. The temperature and pressure effects on flux are pvovided in Figures 9 and 10. 

Figure 3. Effects of transfilter flow and filter pressure on juice flux. Pressure held constant at 250 kPa in upper figure and transfilter flow held constant at 3 m/s in lower figure.

FIGURE 20.4-12 Demonstration of the flux-depressing effects of a smell (117 mm Hg) partial pressure of isopentane in the upstream feed stream for COj permeating through polycarbonele at 35 °C/7... 

Effect of Subcooling. The critical heat flux increases approximately linearly with increasing inlet subcooling over a wide range of subcooling, and for constant mass flux, pressure, and tube length as illustrated in Fig. 15.116. 

For small applied pressures the solvent flux through the membrane is proportional to the applied pressure. Flowever, as the pressure is increased further, the flux begins to drop below that which would result from a linear flux-pressure behavior (Fig. 5.6.1). For macromolecular solutes this nonlinear behavior may be ascribed to concentration polarization, that is, the buildup of rejected solute at the membrane surface. This buildup increases the local osmotic pressure and leads to a lower effective driving pressure and, hence, lower flux, as was shown for reverse osmosis. For macromolecular solutes the... 

The Resistance in Series Model describes the flux of a fouled membrane. This is given in equation (3.4). The resistances Ra>, Ri> and Rc denote the additional resistances which result from the exposure of the membrane to a solution containing particles or solute. Rcp is the resistance due to concentration polarisation, Ri> the internal pore fouling resistance, and Rc the resistance due to external deposition or cake formation. These resistances are usually negligible in RO, where the osmotic pressure effects become more important (Fane (1997)). However, the osmotic pressure can also be incorporated into Rcp. 

The choice of membrane for fouling and rejection studies is crucial. Ko and Pellegrino (1992) pointed out that some membranes exhibit low fouling regardless of their rejection. For other membranes, their flux is controlled b5" osmotic pressure effects, which is indicative of rejection. Laine et al. (1989) pointed out that the most important membrane characteristic is probably hydrophilicity. 

Secondly, the high flux of this membrane could cause severe concentration polarisation and membrane-solute interaction, or fouling (thus reach a critical flux where deposition starts to control flux). This effect can be controlled by variation of the transmembrane pressure and thus flux. 

Overall, the flux ratios (J/Jwo, solution flux after filtration of 120 mL of solution relative to the pure water flux before the experiment) correspond well to the salt rejection. This indicates a concentration polarisation and osmotic pressure effect due to the accumulation of ions at the membrane surface and an increase in cell concentration. This flux decline was fully reversible. The flux of the CA-UF membrane consistently increases after salt filtration, probably due to an increased hydrophilicity after ion adsorption in the membrane. Rejection of calcium is stable and generally does not increase with the concentration in the feed cell. 

The CA-UF membrane has the lowest rejection of organics, and the ion rejection is slightly increased compared to the absence of organics. This may indicate interactions between the retained organics and the cations. This membrane shows a very interesting flux behaviour, with no decline at all over the experiments and a higher pure water flux after the experiments. This indicates the lack of concentration polarisation or osmotic pressure effect at the low salt rejection. The smooth membrane surface would also influence this. The adsorption of ions or organics render the membrane more hydrophilic. 

It is surprising that the TFC-SR membrane does not show this osmotic pressure effect as much as the other membranes, as this membrane also retains a considerable amount of salt (but less sodium). It was calculated in Table 7.22 that sodium is the main contributor to osmotic pressure. However, the flux behaves as if sodium and calcium were virtually absent (compare with TFC-S membrane in absence of sodium and calcium in Figure 7.17). 

The lack of stirring indeed showed that concentration polarisation (which is increased in the absence of stirring) increases flux decline tremendously, even though the membrane appeared less sensitive to osmotic pressure effects. With the flux decline at unstirred conditions, a very significant deposit was... 

In MF, where sieving is believed to dominate rejection, charge effects were observed. However, it is the coUoid stability that determines rejection for colloids which were smaller than membrane pore size. Aggregates that form in the absence of organics are retained, but exhibit reduced rejection at high fluxes, pressures and after a backwash. 

Gallucci F, De Falco M, Tosti S, Marrelli L, Basile A (2007) The effect of the hydrogen flux pressure and temperature dependence factors on the membrane reactor performances. Int J Hydrogen Energy 32 4052-4058... 

Figure 11.10 shows the effect of varying CO partial pressure on the hydrogen flux. No effect of CO on the hydrogen flux is noted as opposed to some... 

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