Effects of the concentration-dependent density on liquid separation in a thermal-diffusion column

Shevtsova

2007

Physics of Fluids

The theoretical framework for describing the multicomponent mixtures with the Soret effect is revised and extended. The separation ratio, a fundamental parameter characterizing the influence of thermal diffusion on convective phenomena, is generalized to the multicomponent case. It is shown how to define this parameter for a particular component of the mixture. To characterize multicomponent system as a whole, the net separation ratio ⌿, which does not depend on the choice of solvent, is introduced. Based on these results, the dimensionless equations for convection in multicomponent mixture are derived. The proposed formulation is applied to analyzing the steady state separation in the thermogravitational column ͑TGC͒. The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The distributions of velocity, temperature, and composition in a multicomponent system are found. The relevant parameters here are the solutal Rayleigh numbers, which characterize the vertical separation of species, and the net solutal Rayleigh number R, which quantifies the overall effect of this separation on the system behavior. It is shown that the key relation of TGC theory, which relates the vertical compositional gradients to the thermal diffusion coefficients, reduces to the dependence of ⌿ on R. A detailed study of this dependence is performed. The evolution of vertical velocity and density profiles with changing the net separation ratio is investigated. It is shown that the solution is unique for ⌿տ−1, nonunique for −5 Շ⌿Շ−1, and does not exist for ⌿Շ−5. A particular ternary mixture is considered and its behavior in the column is analyzed.

Section: Introductionmentioning

confidence: 99%

On thermal diffusion and convection in multicomponent mixtures with application to the thermogravitational column

Shevtsova

2007

Physics of Fluids

On the separation of multicomponent mixtures in a cylindrical thermogravitational column

Kozlova

2016

Physics of Fluids

This work studies the stationary separation of a multicomponent mixture in a thermogravitational column (TGC). The existing theory for a flat-plate column is extended to the case of a cylindrical column. The equations of motion and heat/mass transfer are written in cylindrical coordinates to take into account the impact of the cylinders curvature and the ratio of their radii on the separation process. To characterize the impact of each component on convective motion induced by thermal diffusion, the dimensionless separation ratios are used. A multicomponent system as a whole is described by the net separation ratio. The approximation neglecting vertical diffusion in the column is employed and conditions for its validity are analyzed. The profiles of velocity, temperature, composition, and density in the column with a multicomponent mixture are found and their dependence on the separation ratios and the ratio of cylinders radii is analyzed. The vertical separation is described by the solutal Rayleigh numbers, which are proportional to the vertical concentration gradients. It is shown that the key relation of TGC theory, which relates the net solutal Rayleigh number to the net separation ratio, essentially depends on the ratio of cylinders radii. The working formulas for the thermal diffusion coefficients are derived and the importance of forgotten effect is discussed. It is found that the vertical separation in the column increases with decreasing the ratio of inner and outer cylinders radii. A detailed comparison of results with the case of a flat-plate column is performed. Example of a ternary hydrocarbon mixture is analyzed on the basis of obtained solution and numerical simulation.

Convective stability of multicomponent fluids in the thermogravitational column

Shevtsova

2009

Phys. Rev. E

A comprehensive linear stability analysis of convection in the thermogravitational column is first performed for multicomponent fluids. Two types of perturbations are investigated: Longitudinal waves propagating in vertical direction of the column and transversal waves propagating perpendicular to the vertical axis and temperature gradient. The stability problems are reduced to those without cross-diffusion effect by a special transformation. The calculations are performed for binary and ternary mixtures by the Galerkin method. It is found that in binary fluids, the onset of longitudinal instability can be monotonic or oscillatory depending on the separation ratio, which characterizes the Soret effect. The difference between stability characteristics of binary and ternary fluids is associated with different diffusion times of components in a ternary system. It is shown that the mechanism of transversal instability is related to the unstable density stratification in the column (in total or due to individual components). The unstable stratification can only be realized in fluids with negative Soret effect. The analogue of exchange of stabilities principle for a plane column with a multicomponent fluid is proved. The obtained results indicate that the thermogravitational column can be used for measuring diffusion and thermal diffusion coefficients in ternary and higher mixtures with one or several components having negative Soret effect.