Steady-state species separation in transversally confined thermogravitational columns

Abstract

This work investigates the impact of transverse confinement on the separation of binary positive liquid components in thermogravitational columns through theoretical, numerical, and experimental approaches. Using the three-dimensional parallel flow approximation, the theoretical analysis reveals that in the steady-state, the species separation increases both by the decrease in the transverse aspect ratio of the cavity (B) and by the increase in the product of the Rayleigh number (Ra) and the Lewis number (Le). In particular, we determined a specific value depending on B, which marks the regime where convection overtakes vertical diffusion. In this state, the separation ratio of species obtained from three-dimensional analysis and that predicted by Furry–Jones–Onsager (FJO) theory coincides, regardless of the thermophysical properties of the mixture and the imposed temperature difference between the vertical walls. Using optical digital interferometry, experiments were carried out in thermogravitational microcolumns with transverse aspect ratios B = 5.88 and B = 1.69 for 1,2,3,4-tetrahydronaphthalene |dodecane (C12) and 1,2,3,4-tetrahydronaphthalene|isobutylbenzene mixtures (mass fraction 0.50|0.50) considering three different conditions. Reasonable agreement is observed among the experimental, analytical, and numerical results. Thus, we propose a correlation law for steady-state species separation. This approach offers an alternative to the commonly used FJO theory and provides a reliable method for determining the thermodiffusion coefficient from steady-state species separation measurements.