On the prediction of ultimate separation in parametric pumps

Abstract

Quantitative theories based on first principles are derived to explain the roles of heat and mass transfer in the attainment of steady state or ultimate separation in closed direct-thermal-mode parametric pumps. The theoretical results are in agreement with applicable experimental data, including the experimental anomaly called reversed separation. Under conditions when the axial dispersion is much greater than molecular diffusion, the theory predicts and experiments confirm that l/ln(a,) varies in a linear way with fluid displacement at constant frequency. An additional asymptotic result suggests that when Sh >> PeM, there is a simple linear connection between l/ln(a,) and PeM which is supported by experimental data. , 1975). Moreover, the question of phase difference has never been given a firm theoretical footing. In the present study we undertake to answer these questions.In the direct-thermal-mode of operation, a solid ad-:orbent with a temperature-dependent affinity for the solute to be senarated is used as a retardation media, while periodic fluid motion pumps the lean solvent phase (co'd cycle) and rich solute phase (hot cycle) to their respec5ve reservoirs. During the first part of a cycle, the steps involved include first the transient cooling of the packed bed; this causes solute migration from the bulk phase to the solid adcorbent. In this journey, the solute is retarded by a film resistance at the surface of the solid and disper.zed by the action of the anplied fluid motion. Some rolute moves into the solid by pore diffusion, adsorbing on the pore walls along the way.In the second part of the cycle (hot cycle), the solute de-orbs and wends its way back to the bulk phase in exact reverse of the preceding steps. The rate of solute movement depends on the local bed temperature, which determines the equilibrium driving force for mass transfer. This fundamental picture has been recently used (Rice, 1975) to evolve a quantitative theory to predict the magnitude of concentration difference at ultimate separa!ion (1 --i; n) between the lean and rich reservoirs in a parametric pump. Notwithstanding the reasonable comparison with experiment using only parameters calculated from first principles, there are serious questions regarding the generality of this theory, especially the assumption that the axial concentration profile is linear. Furthermore, the aforementioned theory precludes the occurrence of an equilibrium pinch type of thermodynamic l'mitation, since the form taken by the linearized adsorption isotherm is zuch that at different temperatures, isotherms are required to be parallel.The analytical model presented in the present study differs from the former approach in several respects. While building on the apparent successes of the earlier model (Rice, 1975), we derived a more realistic axial concentration profile to show an exponential dependence. Furthzrmore, equilibrium isotherms were not assumed to b,-parallel. Finally, as a strong test for the new theory, the curious reversed-se:>aration pheno...

Modeling of Ion-Exchange for Cesium Removal From Dissolved Saltcake in SRS Tanks 1-3, 37 and 41

“…For each ion species considered, the Wilson and Geankoplis (1966) correlation is expressed as: A standard deviation of approximately 25% is reported for Eq. (7-1) by Wilson and Geankoplis (1966), while from comparison to the various correlations presented by Foo and Rice (1975) a standard deviation of 100% to 200% is observed.…”

“…With respect to published literature this is a very low Reynolds number range. Numerous mass transfer correlations exist as discussed by Foo and Rice (1975). One of the correlations compared in Foo and Rice (1975) is one developed by Wilson and Geankoplis (1966) based on low Reynolds number data.…”

“…Numerous mass transfer correlations exist as discussed by Foo and Rice (1975). One of the correlations compared in Foo and Rice (1975) is one developed by Wilson and Geankoplis (1966) based on low Reynolds number data. Large variations between correlations exist; however, the sensitivity of VERSE-LC results to the film coefficient has typically been low.…”

Preliminary Ion Exchange Modeling for Removal of Technetium from Hanford Waste Using SuperLig 639 Resin

“…For each ion species considered, the Wilson and Geankoplis (1966) correlation is expressed as: A standard deviation of approximately 25% is reported for Eq. (8-1) by Wilson and Geankoplis (1966), while from comparison to the various correlations presented by Foo and Rice (1975) a standard deviation of 100% to 200% is observed.…”

“…Numerous mass transfer correlations exist as discussed by Foo and Rice (1975, see their Figure 2). One of the correlations compared in Foo and Rice (1975) is one developed by Wilson and Geankoplis (1966) based on low Reynolds number data. Large variations between correlations can be seen; however, our sensitivity to the film coefficient is low as shown in the section discussing sensitivities.…”