Continuum Mechanics and Thermodynamics

, Volume 29, Issue 2, pp 509–534 | Cite as

A two-fluid model for reactive dilute solid–liquid mixtures with phase changes

  • Martina Costa ReisEmail author
  • Yongqi Wang
Original paper


Based on the Eulerian spatial averaging theory and the Müller–Liu entropy principle, a two-fluid model for reactive dilute solid–liquid mixtures is presented. Initially, some averaging theorems and properties of average quantities are discussed and, then, averaged balance equations including interfacial source terms are postulated. Moreover, constitutive equations are proposed for a reactive dilute solid–liquid mixture, where the formation of the solid phase is due to a precipitation chemical reaction that involves ions dissolved in the liquid phase. To this end, principles of constitutive theory are used to propose linearized constitutive equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations. A particularity of the model is that the mass interfacial source term is regarded as an independent constitutive variable. The obtained results show that the inclusion of the mass interfacial source term into the set of independent constitutive variables permits to easily describe the phase changes associated with precipitation chemical reactions.


Eulerian spatial averaging theory Solid–liquid flows Reactive mixtures Constitutive modeling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Physical-Chemistry, Institute of ChemistryUniversity of Campinas-UNICAMPCampinasBrazil
  2. 2.Fachbereich Maschinenbau, Fachgebiet StrömungsdynamikTechnische Universität DarmstadtDarmstadtGermany

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