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Lattice-Boltzmann equations for describing segregation in non-ideal mixtures

Published online by Cambridge University Press:  26 October 2012

Paulo C. Philippi ,
Keijo K. Mattila ,
Diogo N. Siebert ,
Luís O. E. dos Santos ,
Luiz A. Hegele Júnior  and
Rodrigo Surmas
Paulo C. Philippi*
Affiliation:
Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Keijo K. Mattila
Affiliation:
Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Diogo N. Siebert
Affiliation:
State University of Santa Catarina, 88330-668 Camboriu, Brazil
Luís O. E. dos Santos
Affiliation:
Federal University of Santa Catarina, 89218-000 Joinville, Brazil
Luiz A. Hegele Júnior
Affiliation:
Mechanical Engineering Department, Federal University of Santa Catarina, 88040-900 Florianópolis, SC, Brazil
Rodrigo Surmas
Affiliation:
Petrobras, 21941-915 Rio de Janeiro, Brazil
*
†Email address for correspondence: philippi@lmpt.ufsc.br
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Abstract

In fluid mechanics, multicomponent fluid systems are generally treated either as homogeneous solutions or as completely immiscible parts of a multiphasic system. In immiscible systems, the main task in numerical simulations is to find the location of the interface evolving over time, driven by normal and tangential surface forces. The lattice-Boltzmann method (LBM), on the other hand, is based on a mesoscopic description of the multicomponent fluid systems, and appears to be a promising framework that can lead to realistic predictions of segregation in non-ideal mixtures of partially miscible fluids. In fact, the driving forces in segregation are of a molecular nature: there is competition between the intermolecular forces and the random thermal motion of the molecules. Since these microscopic mechanisms are not accessible from a macroscopic standpoint, the LBM can provide a bridge linking the microscopic and macroscopic domains. To this end, the first purpose of this article is to present the kinetic equations in their continuum forms for the description of the mixing and segregation processes in mixtures. This paper is limited to isothermal segregation; non-isothermal segregation was discussed by Philippi et al. (Phil. Trans. R. Soc., vol. 369, 2011, pp. 2292–2300). Discretization of the kinetic equations leads to evolution equations, written in LBM variables, directly amenable for numerical simulations. Here the dynamics of the kinetic model equations is demonstrated with numerical simulations of a spinodal decomposition problem with dissolution. Finally, some simplified versions of the kinetic equations suitable for immiscible flows are discussed.

JFM classification

Complex Fluids: Complex Fluids Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 564 - 587
Copyright
©2012 Cambridge University Press

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