Temperature polarization coefficient

In VMD, the boundary layer resistance in the permeate side and the contribution of the heat transported by conduction through the membrane are negligible (Lawson and Lloyd, 1996a Bandini et al., 1997 Lawson and Lloyd, 1997). This makes VMD of pure water useful to determine the temperature of the feed solution at the membrane surface (T ), and therefore the boundary layer heat transfer coefficients in the membrane module can be evaluated (Mengual et al., 2004). This helps in selecting the adequate empirical heat transfer correlation of a given MD system, which is a complex task when developing theoretical models to determine the temperature polarization coefficients. 

Mengual et al. have observed an Arrhenius type of dependence of the permeate flux on the feed temperature. An increase in the feed circulation velocity increases the heat transfer coefficient in the liquid boundary layer, which in turn increases the VMD flux due to the reduction in the temperature polarization. Concentration factors increased with a decrease in feed temperature during VMD, and for a decrease of 30°C to 10°C, increase in concentration factors from 7-15.5 to 21-31 were obtained for a highly volatile black currant aroma ester [17]. 

Concentration and temperature polarization can be reduced by the presence of spacers that are mrbulence promoters, which enhance the mass flux by increasing the film heat transfer coefficient. Spacers also change the flow characteristics and promote regions of turbulence thus improving boundary layer transfer [106]. DCMD in spacer-filled channels have been shown to improve flux by 31% 1% than that without spacers. The temperamre polarization coefficients are substantially increased and approach unity when the spacers are used in the channels. 

In this relation, M and fi are mass and polarization coefficients of colliding atoms, and Tq is the gas temperature. The ion-conversion effect takes place as a preliminary stage of recombination not only for simple atomic ions but also for some important molecular ions. Polyatomic ions have very high recombination rates (see Table 2-2), often exceeding 10 cm /s at room temperature, which results in an interesting fact recombination of... 

Vapor permeation differs from pervaporation, as stated above, insofar as the feed mixture to be separated is supplied as a vapor. At least the more-permeable component is kept as close to saturation conditions as possible. Thermodynamically there is no difference between a liquid and ifs equilibrium vapor, the partial vapor pressure and thus the driving force for the transport through the membrane are identical and the same solution-diffusion mechanism is valid. However, the density of the vaporous feed and thus the concentration of molecules per volume is lower by two to three orders of magnitude than that of the liquid. As a consequence the membrane is usually less swollen than when in contact with a liquid feed. As the feed mixture getting in contact with the membrane is already in the vapor phase no phase change occurs across the membrane and thus no temperature polarization will be observed. Concentration polarization, however, is still an issue. Although the diffusion coefficient is much higher in a vapor than in a liquid, this is at least partially outbalanced by the lower density of the vapor, and therefore concentration polarization effects may be observed at all concentrations of the component to be removed. Minimum... 

This equation implicitly represents the dependence of polarization on the applied electric field. Usually, the function P E) can be found numerically with temperature dependent coefficient A and constant B and C. 

A porous polypropylene membrane with a water permeability coefficient of 4.2 m/s.bar is used in membrane distillation. Calculate the pure water flux for a feed temperature of 50 C and 90°C, respectively. The temperature at the permeate (distillate) side is 20°C. Neglect temperature polarization. 

Since the first term of the right hand side of equation (11) can be considered a constant, the temperature coefficient of the refractive index An / AT is a measure of the difference between the electronic polarization coefficient and the volumetric thermal expansion coefficient p, where and p are defined as ... 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Note 4. The Number of Dipoles per Unit Volume (Sec. 98). Between 25 and 100°C the value of 1 /t for water rises from TV to , while the increment in the value of l/(t — 1) is nearly the same, namely, from rs to TfV- Similarly in any solvent whose dielectric constant is large compared with unity the temperature coefficients of l/(e — 1) and of 1/e are nearly equal. In comparing the behavior of different solvents, let us consider now how the loss of entropy in an applied field will depend upon n, the number of dipoles per unit volume. Let us ask what will be the behavior if (e — 1) is nearly proportional to n/T as it is in the case of a polar gas. In this case we have l/(e — 1) nearly proportional to T/n and since in a liquid n is almost independent of T, wc have... 

In general terms, the pyroelectric coefficient of a free sample consists of three components. The first, called the real coefficient, depends on the derivative of spontaneous polarization with respect to the temperature. The second is derived from the temperature dilatation and can be calculated based on mechanical parameters. The third coefficient is related to the piezoelectric effect and results from the temperature gradient that exists along the polar axis of the ciystal. 

The hiding of the pyroelectric coefficients seems to be correlated to the maximum c parameter, which in turn corresponds to the transition temperature. The shift along the Oz direction, Az, of the niobium atoms, which are located within the octahedrons, is responsible for the compound s polar properties. When c is at its maximum, this shift is enhanced and leads apparently to maximum spontaneous polarization P The value of Ps increases in the temperature range of 300 to 490K and then decreases at temperatures above 490°K. 

It is easily possible to introduce refinements into the dilated van Laar model which would further increase its accuracy for correlating activity coefficient data. However, such refinements unavoidably introduce additional adjustable parameters. Since typical experimental results of high-pressure vapor-liquid equilibria at any one temperature seldom justify more than two adjustable parameters (in addition to Henry s constant), it is probably not useful for engineering purposes to refine Chueh s model further, at least not for nonpolar or slightly polar systems. 

Finally, the brominations of mesitylene, 1,2,4,5-tetramethyl- and pentamethyl-benzene in chloroform (which is more polar than carbon tetrachloride) are first-order in bromine and iodine monobromide318, so that this is entirely consistent with the pattern developed above, i.e. the more polar the solvent and the more reactive the compound, the fewer the number of molecules of iodine monobromide that are involved in the rate-determining step. Measurements of rates between 25 and 42 °C revealed no significant trend owing to the variability of the rate coefficients determined at any temperature, but even so it is clear that there is no appreciable activation energy for these compounds, and there may have been temperature inversion for some of them. 

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