Interfacial flux constitutive equation

The condition of local mass equilibrium can exist even when adsorption and chemical reaction are taking place (Whitaker, 1999, Problem 1-3). When local mass equilibrium is not valid, one must propose an interfacial flux constitutive equation. The classic linear form is given by (Langmuir, 1916, 1917)... 

When the temperature is not constant, the bulk heat transfer equation complements the system and involves Equations 5.240, 5.241, and 5.276. The heat transfer equation is a special case of the energy balance equation. It should be noted that more than 20 various forms of the overall differential energy balance for multicomponent systems are available in the literature." " The corresponding boundary condition can be obtained as an interfacial energy balance." - Based on the derivation of the buUc and interfaciaT entropy inequalities (using the Onsager theory), various constitutive equations for the thermodynamic mass, heat, and stress fluxes have been obtained. 

In spite of the wide variety of interfacial media encountered, it is possible in many cases to obtain surface balance equations, which are representative and unrestrictive in comparison to actual phenomena. The constitutive laws can be established by dimensional analysis. They relate to surface variables, to flux and rates of production. The phenomenological coefficients can be determined experimentally, or by detailed analysis over the interfacial thickness. The solution implies a coupling between these equations and those for volumes in contact. In the examples presented here, the results are in perfect agreement with those of simple classical theory. 

These models consider either the thermodynamic or mechanical non-equilibrium between the phases. The number of conservation equations in this case are either four or five. One of the most popular models which considers the mechanical non-equilibrium is the drift flux model. If thermal non-equilibrium between the phases is considered, constitutive laws for interfacial area and evaporation/condensation at the interface must be included. In this case, the number of conservation equations is five, and if thermodynamic equilibrium is assumed the number of equations can be four. Well-assessed models for drift velocity and distribution parameter depending on the flow regimes are required for this model in addition to the heat transfer and pressure drop relationships. The main advantage of the drift flux model is that it simplifies the numerical computation of the momentum equation in comparison to the multi-fluid models. Computer codes based on the four or five equation models are still used for safety and accident analyses in many countries. These models are also found to be useful in the analysis of the stability behaviour of BWRs belonging to both forced and natural circulation type. 

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