An eigenvalue method for determination of multicomponent diffusion coefficients. Application to NaOH + NaCl + H₂O mixtures

Abstract

A general method for the determination of multicomponent diffusion coeff~cients is developed using the algebraic technique of matrix diagonalization. When linear combinations of measurements from several multicomponent diffusion experiments performed with different initial concentration gradients (but with the same final composition) are analyzed as simple binary data, particular combinations may be found that transform the multicomponent diffusion coefficient matrix D to diagonal form and thus yield time-invariant. pseudo-binary diffusion coefficients: the eigenvalues of D. Since the matrix that diagonalizes D is given by the coefficients used to form the linear combinations, D is easily recovered by the inverse transformation. The advantages of the eigenvalue method are briefly discussed. For testing purposes, ternary diffusion coefficients are determined from conductance measurements for d~lute aqueous NaOH + NaCl mixtures. Diffusion of NaOH in aqueous NaCl is significantly more rapid than in pure water, and large coupled flows of NaCl are observed. The results are in close agreement with behavior predicted by Onsager-Fuoss theory. 476 (1985). Faisant appel i une technique algkbrique de diagonalisation des matrices, on a developpe une mCthode gkntrale permettant de determiner les coefficients de diffusion i plusieurs composantes. Lorsqu'on analyse, sous forme de donnkes binaires simples, des combinaisons linkaires de mesures provenant de plusieurs expCriences de diffusion i plusieurs composantes, rkaliskes avec des gradients diffkrents de concentrations initiales (mais avec la meme composition finale), on peut trouver des combinaisons particulikres qui permettent de transformer en une forme diagonale la matrice D du coefficient de diffusion i plusieurs composantes; on peut ainsi obtenir des coefficients de diffusion peudo-binaires qui ne varient pas avec le temps.Puisque la matrice qui diagonalise D est obtenue i partir des combinaisons utilisees pour former Ies combinaisons lineaires.on peut facilement rtcupkrer D par la transformation inverse. On discute brikvement des avantages de la mCthode des valeurs de eigen. Pour fins de verification, on a determink les coefficients de diffusion ternaires i partir de mesures de conductivitt sur des solutions aqueuses diluees de mClanges de NaOH + NaCI. La diffusion du NaOH dans le NaCl aqueux est beaucoup plus rapide que dans I'eau pure et on observe d'importantes migrations couplCes de NaCI. Les rksultats obtenus sont en bon accord avec le comportement prCdit par la thCorie de Onsager-Fuoss.[Traduit par le journal]I. Introduction Multicomponent diffusion is of theoretical interest and considerable practical importance ( 1 , 2). In many cases the diffusivity of a solute in a multicomponent mixture is significantly different from its binary diffusivity, especially if the solutes are electrolytes or they react chemically (3-8). Moreover, because diffusional flows interact, multicornponent diffusion of a component produces countercurrent or cocurrent flows of other compo...

Ternary Diffusion Coefficients of Cyclohexane + Toluene + Methanol by Taylor Dispersion Measurements at 298.15 K. Part 1. Toluene-Rich Area

“…Mass transport by diffusion is a fundamental process that plays an important part in chemistry and chemical engineering in processes such as liquid extractions, solid extraction, distillation, and chemical reactions as well as biological systems. Different experimental methods are established to measure diffusion coefficients: diaphragm cell, − conductometric , and optical − (e.g., Gouy-, Rayleigh-, and holographic interferometry), and dynamic light scattering (DLS). − A fast and simple method compared with optical techniques, the Taylor dispersion technique is well established in the case of binary mixtures of organic compounds and of electrolyte solutions. − With this method, it is also possible to investigate diffusion processes in ternary systems. − However, the fact that in organic liquid systems one experimentally measurable quantity, the refractive index, has to be used to extract two eigenvalues or four elements of the matrix of ternary mutual diffusion coefficients demonstrates the considerably higher complexity of the ternary diffusion problem, and as a consequence, publications of ternary diffusion coefficients are rather rare.…”

“…Mass transport by diffusion is a fundamental process that plays an important part in chemistry and chemical engineering in processes such as liquid extractions, solid extraction, distillation, and chemical reactions as well as biological systems. Different experimental methods are established to measure diffusion coefficients: diaphragm cell, 1-5 conductometric 6,7 and optical [8][9][10][11][12] (e.g., Gouy-, Rayleigh-, and holographic interferometry), and dynamic light scattering (DLS). [13][14][15][16] A fast and simple method compared with optical techniques, the Taylor dispersion technique is well established in the case of binary mixtures of organic compounds and of electrolyte solutions.…”

Ternary Diffusion Coefficients of Glycerol + Acetone + Water by Taylor Dispersion Measurements at 298.15 K

“…To investigate diffusion phenomena, different experimental methods are established: diaphragm cell, − conductometric, , and optical − (e.g., Gouy, Rayleigh, and holographic interferometry and also dynamic light scattering for the measurement of mutual diffusion coefficients − ).…”

The onset of convective instability in a triply diffusive fluid layer

“…threecomponent) fluids (McDougall 1983 ;Miller & Vitagliano 1986 ;Wells 1986), in which there are four independent diffusion coefficients (including cross-terms). Lcaist & , Noulty (1985) have suggested that the tools are now available for measurement of the nine diffusion coefficients characterizing a quaternary (four-component) fluid, for which the relevant theory was developed earlier by Kim (1966Kim ( , 1969, and have now measured the nine independent quaternary diffusion coefficients in the system H,O-KCl-KH,PO,-H,PO, (Noulty & Leaist 1987). In this case, as well as in the case of a non-isothermal ternary fluid, there are three independently diffusing stratifying agencies.…”