Kjetil B. Haugen

On measurement of thermal diffusion coefficients in multicomponent mixtures

We investigate the steady-state separation of the individual components of an incompressible multicomponent liquid mixture in a narrow two-dimensional thermogravitational column. Analytic working equations for measuring thermal diffusion coefficients analogous to the existing equations for a binary mixture are derived. Similar to the binary results, we find that when compositional variation has negligible effect on fluid density and vertical diffusive flux can be ignored, molecular diffusion does not affect steady-state separation. However, when compositional effects on density are taken into account, molecular diffusion does affect the bulk convective flow and the steady-state separation of the components. There may be also two distinct trends in the velocity and separation profiles. With one or more negative thermal diffusion coefficients, there may be more than one convection cell resulting in oscillatory behavior of separation. The working equations presented can be used to measure thermal diffusion coefficients of multicomponent mixtures. Such measurements have not yet been reported in the literature.

Composition at the interface between multicomponent nonequilibrium fluid phases

The computation of mass transfer between two nonequilibrium phases requires interfacial composition. For a system with a total of M components, the assumption of local thermodynamic equilibrium provides only M equations while the number of unknown interfacial compositions is 2(M-1). In binary systems (M=2), the number of equations matches the number of unknowns and the interfacial composition is readily computed at any temperature and pressure. In multicomponent systems (M>or=3), the number of unknowns exceeds the number of equations and additional constraints are required. To the best of our knowledge, a general solution to the problem of computing interfacial composition in multicomponent systems has not been presented in the past, despite its fundamental importance. In this work we present a general and consistent method of computing interfacial composition where the additional constraints are obtained from mass balance across the interface. The derivations reveal that in multicomponent systems interfacial composition depends on the diffusion coefficients in the two bulk phases. This is a fundamental difference from binary systems. The differences are demonstrated by comparing examples of mixing of nonequilibrium phases in binary and ternary (M=3) systems.

On the unsteady-state species separation of a binary liquid mixture in a rectangular thermogravitational column

This paper investigates the unsteady-state species segregation of binary liquid mixtures in rectangular thermogravitational columns. The analysis leads to a procedure to obtain both molecular and thermal diffusion coefficients from transient separation measurements. Two models are presented: first, an ideal model where buoyancy only depends on temperature and second, a general model where buoyancy also varies with composition. Steady-state measurements are not required regardless of which model is chosen. As a result, the new procedure is faster than steady-state procedures. When either the molecular or thermal diffusion coefficient is known a priori, the other can be obtained without knowledge of fluid properties such as density, viscosity, thermal expansion, and compositional coefficients.

Transient separation of multicomponent liquid mixtures in thermogravitational columns

Transient separation of the individual components in a multicomponent liquid mixture in a thermogravitational column can be used to determine the thermal and molecular diffusion coefficients. Two models of the transient behavior are developed. First, a classical model where density only depends on temperature. Second, a general model where the compositional effect on density is also taken into account. Diffusion coefficients can be determined by fitting experimental data to either model. The procedure is demonstrated for a ternary liquid mixture. The results reveal that the classical model is very unreliable even though composition variation only contributes to the total buoyancy by one-third. Diffusion coefficients can be obtained reliably from the general model provided the experimental noise does not exceed +/-1% of steady-state separation. This level of accuracy in composition measurements is achievable.