References
- S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, chap. XI, 2nd ed., Dover, New York, 1984.
- J. C. Maxwell, On the Dynamic Theory of Gases, Philos. Trans. R. Soc., vol. 157, pp. 49–88, 1867.
- J. Stefan, Uber das Gleichgewicht und die Bewegung Insbesondere die Diffusion von Gasgemengen, Akad. Wiss. Wien, vol. 63, pp. 63–124, 1871.
- R. Taylor and R. Krishna, Multicomponent Mass Transfer, pp. 13–94, Wiley, New York, 1993.
- J. Mitrovic, The Fick and Lagrange Equations as a Basis for the Maxwell – Stefan Diffusion Equations, Int. J. Heat Mass Transfer, vol. 40, pp. 2373–2377, 1997.
- C. F. Curtiss and R. B. Bird, Multicomponent Diffusion, Ind. Eng. Chem. Res., vol. 38, pp. 2515–2522, 1999.
- S. H. Lam, Multicomponent Diffusion Revisited, Phys. Fluids, vol. 18, art. no. 073101, 2006.
- Y. Wang and M. D. LeVan, Mixture Diffusion in Nanoporous Adsorbents: Equivalence of Fickian and Maxwell-Stefan Approach, J. Phys. Chem. B, vol. 112, pp. 8600–8604, 2008.
- Gh. Juncu, A. Nicola, C. Popa, and E. Stroila, Preconditioned Conjugate Gradient and Multi-Grid Methods for Numerical Solution of Multi-Component Mass Transfer Equations. I. Diffusion – Reaction Equations, Numer. Heat Transfer A, vol. 66, pp. 1268–1296, 2014.
- Gh. Juncu, A. Nicola, C. Popa, and E. Stroila, Preconditioned Conjugate Gradient and Multi-grid Methods for Numerical Solution of Multi-Component Mass Transfer Equations. II. Convection - Diffusion – Reaction Eequations, Numer. Heat Transfer A, vol. 66, pp. 1297–1319, 2014.
- J. M. Stockie, K. Promislow, and B. R. Wetton, A Finite Volume Method for Multicomponent Gas Transport in a Porous Fuel Cell Electrode, Int. J. Numer. Meth. Fluids, vol. 41, pp. 577–599, 2003.
- E. Leonardi and C. Angeli, Transient Diffusion within Spherical Particles: Numerical Resolution of the Maxwell – Stefan Formulation, Ind. Eng. Chem. Res., vol. 49, pp. 5654–5660, 2010.
- E. Kozeschnik, Multicomponent Diffusion Simulation Based on Finite Elements, Metall. Mater. Trans. A, vol. 30A, pp. 2575–2582, 1999.
- W. III. Wangard, D. S. Dandy, and B. J. Miller, A Numerically Stable Method for Integration of the Multicomponent Species Diffusion Equations, J. Comput. Phys., vol. 174, pp. 460–472, 2001.
- S. Mazumder, Critical Assessment of the Stability and Convergence of the Equations of Multi-Component Diffusion, J. Comput. Phys., vol. 212, pp. 383–392, 2006.
- A. Kumar and S. Mazumder, Coupled Solution of the Species Conservation Equations Using Unstructured Finite-Volume Method, Int. J. Numer. Meth. Fluids, vol. 64, pp. 409–442, 2010.
- Gh. Juncu, Unsteady Ternary Mass Transfer from a Sphere in Creeping Flow, Int. J. Therm. Sci., vol. 44, pp. 255–266, 2005.
- H. L. Toor, Solution of the Linearized Equations of Multicomponent Mass Transfer: Matrix Methods, A.I.Ch. E. J., vol. 10, pp. 460–465, 1964.
- W. E. Stewart, and R. Prober, Matrix Calculation of Multicomponent Mass Transfer in Isothermal Systems, Ind. Eng. Chem. Fundam., vol. 3, pp. 224–235, 1964.
- G. J. McRae, W. R. Goodin, and J. H. Seinfeld, Numerical Solution of the Atmospheric Diffusion Equation for Chemically Reacting Flows, J. Comput. Phys., vol. 45, pp. 1–42, 1982.
- R. I. McLachlan, G. Reinout, and W. Quispel, Splitting Methods, Acta Numerica, vol. 11, pp. 341–434, 2002.
- R. C. Cabrales, F. Guillén-González, and J. V. Gutiérrez-Santacreu, A Time – Splitting Finite – Element Stable Approximation for the Ericksen – Leslie Equations, SIAM J. Sci. Comput., vol. 37, pp. B261–B282, 2015.
- W. Xie, H. Li, Z. Tian, and S. Pan, A Low Diffusion Flux Splitting Method for Inviscid Compressible Flows, Comput. Fluids, vol. 112, pp. 83–93, 2015.
- S. Zhai, Z. Weng, and X. Feng, Investigations on Several Numerical Methods for the Non-local Allen-Cahn Equation, Int. J. Heat Mass Transfer, vol. 87, pp. 111–118, 2015.
- N. Crouseilles, M. Kuhn, and G. Latu, Comparison of Numerical Solvers for Anisotropic Diffusion Equations Arising in Plasma Physics, J. Sci. Comput., vol. 65, pp. 1091–1128, 2015.
- G. I. Marchuk, Methods of Numerical Mathematics, Springer, chap. 5, New York, 1975.
- G. I. Marchuk Splitting and Alternating Direction Methods, in P. G. Ciarlet and J. L. Lions (eds.), Handbook of Numerical Analysis, vol. I, pp. 199–462, Elsevier, North – Holland, 1990.
- W. J. Korchinsky, P. Grassia, and C. H. Harrison, Multicomponent Mass Transfer in Films and Rigid Drops: The Influence of Concentration-Variable Diffusivity, Chem. Eng. Sci., vol. 64, pp. 433–442, 2009.
- S. Ubal, C. H. Harrison, P. Grassia, and W. J. Korchinsky, Numerical Simulation of Mass Transfer in Circulating Drops, Chem. Eng. Sci., vol. 65, pp. 2934–2956, 2010.
- S. Ubal, P. Grassia, C. H. Harrison, and W. J. Korchinsky, Numerical Simulation of Multi-Component Mass Transfer in Rigid or Circulating Drops: Multi-Component Effects Even in the Presence of Weak Coupling, Colloids Surf A Physicochem. Eng. Aspects, vol. 380, pp. 6–15, 2011.
- S. Ubal, P. Grassia, C. H. Harrison, and W. J. Korchinsky, Reprint of Numerical Simulation of Multi-Component Mass Transfer in Rigid or Circulating Drops: Multi-Component Effects Even in the Presence of Weak Coupling, Colloids Surf A Physicochem. Eng. Aspects, vol. 382, pp. 251–260, 2011.
- R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops and Particles, chap. 3, Academic Press, New York, 1978.
- L. G. Leal, Advanced Transport Phenomena, chap. 7, Cambridge University Press, Cambridge, 2007.
- D. L. Ropp and J. N. Shadid, Stability of Operator Splitting Methods for Systems with Indefinite Operators: Advection – Diffusion – Reaction Systems, J. Comput. Phys., vol. 228, pp. 3508–3516, 2009.