Solidification and separation in saline water

Mauro  Fabrizio; Claudio Giorgi; Angelo  Morro

doi:10.3934/dcdss.2016.9.139

Article Contents

2016, Volume 9, Issue 1: 139-155. Doi: 10.3934/dcdss.2016.9.139

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Solidification and separation in saline water

1.
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S.Donato 5, 40127 Bologna
2.
DICATAM, Università degli studi di Brescia, Via D.Valotti 9, 25133 Brescia
3.
DIBRIS, Università di Genova, Via Opera Pia 13, 16145 Genova

Received: August 31, 2014

Revised: January 31, 2015

Published: January 2016

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Abstract

Motivated by the formation of brine channels, this paper is devoted to a continuum model for salt separation and phase transition in saline water. The mass density and the concentrations of salt and ice are the pertinent variables describing saline water. Hence the balance of mass is considered for the single constituents (salt, water, ice). To keep the model as simple as possible, the balance of momentum and energy are considered for the mixture as a whole. However, due to the internal structure of the mixture, an extra-energy flux is allowed to occur in addition to the heat flux. Also, the mixture is allowed to be viscous. The constitutive equations involve the dependence on the temperature, the mass density of the mixture, the salt concentration and the ice concentration, in addition to the stretching tensor, and the gradient of temperature and concentrations. The balance of mass for the single constituents eventually result in the evolution equations for the concentrations. A whole set of constitutive equations compatible with thermodynamics are established. A free energy function is given which allows for capturing the main feature which occurs during the freezing of the salted water. That is, the salt entrapment in small regions (brine channels) where the cryoscopic effect forbids complete ice formation.

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Mathematics Subject Classification: Primary: 76T99; Secondary: 74F20, 82C26, 82D15.

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