Experiments solute reflection coefficient

Typical results of an ultrafiltration experiment also reflect the presence of concentration polarization. This phenomenon, l.e. accumulation of solute in front of the membrane, was described in great detail by others (Refs. 3, 4). A consequence of concentration polarization is a strong dependence of measured rejection coefficients on transmembrane fluxes. An illustration of the effect is presented in Figure 9, which shows the measured "apparent" rejection coefficients (Rg) as a function of transmembrane flux for two water-soluble polymers (Tetronic 707 and Carbowax 4000). It is clear from Figure 9 that if we want to minimize the effects of concentration polarization, we have to conduct experiments at very low values of transmembrane flux. 

Both coefficients, the solute permeability CD and the reflection coefficient a can be obtained by performing an osmotic and diffusion experiment. Also reverse osmosis can be applied. B rearranging eq. V - 42, the following equation is obtained ... 

The model system described above remains anyhow a simplified model for epithelia, as it neglects diffusive phenomena in the inner compartment and the possibility of coupling between the passive and active solute flows, which can be excluded only in mosaic membranes. In any case the results seem useful in order to explain the experimental data and to obtain a better control of the experiments. In effect, the variability of the filtration, ultrafiltration and apparent reflection coefficients which appear to be a function of both the experimental conditions and of the activity of the epithelia, imposes to be very careful in programming the experiments and when comparing the values existing in literature, often determined in poorly defined conditions. 

The Staverman reflection coefficient, o, measures the extent to which the membrane rejects a given solute purely transported by convection. Solutes fully rejected by the membrane feature o = 1. Solutes freely permeating the membrane feature ct = 0. Membrane rejection toward a given solute is experimentally assessed in the course of pure filtration experiments in terms of its rejection coefficient R, or its sieving coefficient S, with S = —R being the permeate-to-retentate solute concentration ratio. In fact, R is related to a as follows (Spiegler and Kedem, 1996) ... 

In all of these cases, the structure of the organic sorbate, the composition of the surface, and the conditions of the vapor or solution exchanging with the solid must be considered. However, it is important to note that with some experience in thinking about the organic chemicals and environmental situation involved, we can usually anticipate which one or two sorption mechanisms will predominate. For example, in Chapter 9 we wrote an expression reflecting several simultaneously active sorption mechanisms, each with their own equilibrium descriptor, to estimate an overall solid-water distribution coefficient for cases of interest (Eq. 9-16) ... 

The constant /3 contains a partitioning coefficient of the analyte between the solution and the modifying layer, as well as the constants related to the bulk electrolysis in a small volume (i.e., thin) cell (Bard and Faulkner, 2001). If the electroactive species are confined to the electrode, if the couple is perfectly reversible, and if the extraction is fast on the time scale of the experiment, the peaks in the cyclic voltammogram occur at the same potential and the areas (charge) below the cathodic and anodic branches are equal, as is the case in Fig. 7.12. Obviously, any deviations from these conditions are reflected in the shape of the CV curve. Nevertheless, even then the relationship between the peak current iv and the bulk concentration of the electroactive species can be reproducible. In the determination of Fe2+ using the above procedure, the linear calibration between 5 x 10 8 and 5 x 10-6 M concentration has been obtained. 

At this point, we have defined an ideal reference state for the RNA in which there are no net interactions with ions, and introduced the RNA activity coefficient as a factor that assesses the deviation of the RNA from ideal behavior due to its interactions with all the ions in solution. No assumptions have been made about the nature of the ion interactions anions and cations, long- and short-range interactions all contribute. The ion interaction coefficients (Eqs. (21.4a) and (21.4b)) also reflect the ion—RNA interactions that create concentration differences in a dialysis experiment, and there is an intimate relationship between activity coefficients (y) and interaction coefficients (F), as developed below. This relationship will be extremely useful y comes from the chemical potential and gives access to free energies and other thermodynamic functions, while F is directly accessible by both experiment and computation (see Pappu et al., this volume, 111.20). 

The Debye-Huckel theory gives a calculation of the activity coefficients of individual ions. However, although the individual concentrations of the ions of an electrolyte solution can be measured, experiment cannot measme the individual activity coefficients. It does, however, furnish a sort of average value of the activity coefficient, called the mean activity coefficient, for the electrolyte as a whole. The term mean is not used in its common sense of an average quantity, but is used in a different sense which reflects the number of ions which result from each given formula. Such mean activity coefficients are related to the individual activity coefficients in a manner dictated by the stoichiometry of the electrolyte. 

Next, one frequently would like to be able to make some assessment of the accuracy of a set of experimental vapor-liquid or activity coefficient measurements. Basic thermodynamic theory (as opposed to the solution modeling of Chapter 9) provides no means of predicting the values of liquid-phase activity coefficients to which the experimental results could be compared. Also, since the liquid solution models discussed in Chapter 9 only approximate real solution behavior, any discrepancy between these models and experiment is undoubtedly more a reflection of the inadequacy of the model than a test of the experimental results. 

Using liquid/liquid phase separation by thenoyltrifluoracetone, TTA, in benzene, the authors studied the speciation of Zr in the concentration range 10 to 0.1 M in 2 M perchloric acid solution as well as in 1 M HCIO4/I M LiC104 solutions. TTA is known to selectively extract free tetravalent ions such as Zr or the tetravalent actinide ions. Polymer formation by Zr in the aqueous phase is reflected quantitatively as a decrease in the distribution coefficient. The experiments were conducted very carefully spectroscopic determination of species in the benzene phase, correction for TTA loss of the benzene phase, consideration for complexation of Zr by TTA in the aqueous phase, recrystallisation of starting solids, consideration of impurities in the test, assurance that equilibrium has been reached and discussion of errors related to the variation of proton activity in the aqueous phase due to the extraction reaction. 

The results presented in Fig. 12.2 of the chromatographic experiment with the concentrated CaCl2/HCl feed mixture fuUy agree with the distribution coefficients found for the system under static conditions. Indeed, the distance between the elution fronts of HCl and CaCl2 is now much larger than it was in the case of separately eluting the two electrolytes (Fig. 12.1). This fact reflects the increased difference between the phase distribution coefficients of the two components, that is, the increased separation selectivity in the concentrated feed solution. 

The calculation of drying processes requires a knowledge of a number of characteristics of drying techniques, such as the characteristics of the material, the coefficients of conductivity and transfer, and the characteristics of shrinkage. In most cases these characteristics cannot be calculated by analysis, and it is emphasized in the description of mathematical models of the physical process that the so-called global conductivity and transfer coefficients, which reflect the total effect on the partial processes, must frequently be interpreted as experimental characteristics. Consequently, these characteristics can be determined only by adequate experiments. With experimental data it is possible to apply analytical or numerical solutions of simultaneous heat and mass transfer to practical calculations. 

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