Liquid transference numbers

Liquid Hydrocarbon Fuei Mass Transfer Number B... 

The flow capacity of a pump can be expressed as its displacement per revolution or by its output in gallons per minute (gpm). Displacement is the volume of liquid transferred in one complete cycle of pump operation. It is equal to the volume of one pumping chamber multiplied by the number of chambers that pass the outlet during one complete revolution or cycle. Displacement is expressed in cubic inches per revolution. 

Figure 5.47 shows a plot of the ratio of the experimental heat transfer coefficient obtained by Bao et al. (2000) divided by the predicted values of Chen (1966) and Gungor and Winterton (1986) for heat transfer to saturated flow boiling in tubes versus liquid Reynolds number. It can be seen that both methods provide reasonable predictions for Rcls > 500, but that both overpredict the heat transfer coefficient at lower values of Rols- For comparison it was assumed that the boiling term of these correlations is zero. 

The emf of the cell, contrary to that in the absence of a liquid junction, depends on the transference numbers. Such cells are usually identified as concentration cells with presence of transference, the second one in the electrolyte concentration cell classification list. This system, as has been seen, contains a liquid junction across which it is possible for direct transport of ions to occur. 

It is the product of the bubble Reynolds and the liquid Prandtl number divided by the boiling Nusselt number (Nu,), which is equivalent to the Stanton number in single-phase convective heat transfer. 

For the liquid phase, the corresponding number of overall liquid transfer units Noz, is given by ... 

Nl.Nog Number of liquid film and overall liquid transfer units ... 

TABLE 6.1 Transfer Numbers of Various Liquids in Air3... 

In fact, at the pzc, the membrane should show the liquid junction potential [88] based on the transference numbers of the ions in the bulk solution. 

A lithium ion transference number significantly less than 1 is certainly an undesired property, because the resultant overwhelming anion movement and enrichment near electrode surfaces would cause concentration polarization during battery operation, especially when the local viscosity is high (such as in polymer electrolytes), and extra impedance to the ion transport would occur as a consequence at the interfaces. Fortunately, in liquid electrolytes, this polarization factor is not seriously pronounced. 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (Recall that an uncertainty of 1 mV corresponds to a relative error of 4% in the concentration of a monovalent ion.) Since potential measurements are seldom better than 0.1 mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentio-metric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions on both sides of the junction ... 

The formula (VI-29) is valid for any uni-univalent electrolyte. It is evident from this formula that the sign of the liquid junction potential and also the orientation of the diffusion double layer, in respect to the double layer at the electrodes, depends on the relative magnitude of the anion and cation transference numbers. Should the anion transference number exceed that of cation... 

The influence of the relative values of the transference numbers, affecting the resultant value of the EMF of the concentration cell without transference, is clearly to be seen from the equation (VI-29) should t.. > <+ then eK is positive and in a concentration cell reversible with respect to cations the liquid junction potential is added to the sum of the electrode potentials should, however, < t+, then the liquid junction potential will lower the resultant EMF. In a concentration cell reversible with respect to anions (e. g. in a cell with chlorine electrodes) the EMF is decreased when ( >(+, and increased when t. < t+. 

The physical absorption technique (manometric method) is suitable to determine the liquid side volumetric mass transfer coefficient as well as the gas-side one. Results show that kLa is independant of pressure and depends mainly on the system s hydrodynamics and secondly, that koa is inversely proportional to the total pressure and can be related to the liquid Reynolds number. 

The parameter X contains the Damkoehler number, Da, the Stanton number for gas-to-liquid transfer, Stgj the external contact-... 

Self-diffusivity, cooperatively with ionic conductivity, provides a coherent account of ionicity of ionic liquids. The PGSE-NMR method has been found to be a convenient means to independently measure the self-diffusion coefficients of the anions and the cations in the ionic liquids. Temperature dependencies of the self-diffusion coefficient, viscosity and ionic conductivity for the ionic liquids, cannot be explained simply by Arrhenius equation rather, they follow the VFT equation. There is a simple correlation of the summation of the cationic and the anionic diffusion coefficients for each ionic liquid with the inverse of the viscosity. The apparent cationic transference number in ionic liquids has also been found to have dependence on the... 

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