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Non-equilibrium thermodynamic model for calcium carbonate supersaturated solutions of high salinity

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Abstract

Based on principles of non-equilibrium thermodynamics, the behavior of calcium carbonate supersaturated solutions of high salinity is studied. For this purpose, these solutions are treated as continuous media whose physicochemical properties change in space and time. Furthermore, by exploiting the Müller–Liu formulation for the second law of thermodynamics, one recognizes which thermodynamic forces are responsible for keeping the \(CaCO_{3}\) supersaturated solutions out of equilibrium. The obtained results suggest that intermolecular interaction forces play an important role in the dynamics of solution, as well as in the mass transport of solutes. Particularly, from the estimated values for the self-diffusion and mutual diffusion coefficients of NaCl(aq), \(CaCl_{2}(aq)\), and \(Na_{2}CO_{3}(aq)\), one discusses whether changes in the concentration of NaCl(aq) may affect the mass transport of \(Na_{2}CO_{3}(aq)\) and \(CaCl_{2}(aq)\) in calcium carbonate supersaturated solutions. The results of this work may be helpful to understand better the influence of diffusive processes and intermolecular interaction forces on the dynamics of calcium carbonate supersaturated solutions of high salinity.

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Notes

  1. Although the independent constitutive variable is \(\mathbf {u}_{a}\), all differentiations are performed in relation to \(\mathbf {v}_{a}\) and later the relation \(\dfrac{\partial \mathcal {C}}{\partial \mathbf {v}_{a}}=\dfrac{\partial \mathcal {C}}{\partial \mathbf {u}_{a}}-\dfrac{\rho }{\rho _{a}}{\displaystyle \sum _{b=1}^{n}}\dfrac{\partial \mathcal {C}}{\partial \mathbf {u}_{b}}\) is used.

  2. Equation (3.1) may be also written in terms of the gradient of concentration \(\nabla c(a)\) since \(\rho _{a}\) and c(a) are interrelated by the molar mass of species a.

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Authors and Affiliations

  1. Department of Physical Chemistry, Institute of Chemistry, University of Campinas- UNICAMP, Campinas, São Paulo, Brazil

    Martina Costa Reis, Maria de Fátima Brito Sousa, Celso Aparecido Bertran & Adalberto Bono Maurizio Sacchi Bassi

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  1. Martina Costa Reis
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  2. Maria de Fátima Brito Sousa
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  3. Celso Aparecido Bertran
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  4. Adalberto Bono Maurizio Sacchi Bassi
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Correspondence to Martina Costa Reis.

Additional information

The first author acknowledges financial support from the São Paulo Research Foundation (Grant 2013/20872-2).

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Reis, M.C., de Fátima Brito Sousa, M., Bertran, C.A. et al. Non-equilibrium thermodynamic model for calcium carbonate supersaturated solutions of high salinity. J Math Chem 54, 44–60 (2016). https://doi.org/10.1007/s10910-015-0547-x

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