Interfacial Transport Phenomena Closures

The macroscopic multi-phase models resulting from the local averaging procedures must be supplemented with state equations, constitutive equations, boundary and initial conditions. The constitutive equations specify how the phases interact with themselves and with each other. The closure laws or constitutive laws can thus be divided into three types [16] Topological, constitutive and transfer laws, where the first type describes the spatial distribution of phase-specific quantities, the second type describes physical properties of the phases and the third type describes different interactions between the phases. 

The accurate modeling of multiphase flows requires that the phase interaction terms given by the jump conditions are correctly parameterized. This problem is very involved since not all of the phase interaction and phase change terms are independent. Most of the existing expressions are of empirical nature, thus experimental data are needed in order to develop and validate laws. Guiding principles for formulating closure laws are given by [3, 31, 35-37]  

The principle of equipresence states that if one variable is known to depend on one specific variable, then all other variables to be constituted must be allowed to depend on the same variable (i.e. unless another principle shows that a particular dependence cannot occur). This principle prevents a priori prejudicing of the 

The principle of well-posedness states that the description of the motion should be such that a solution to the initial boundary value problem exists and depends continuously on the initial and boundary conditions. 

In mathematical terms this implies that all eigenvalues of the system of Partial Differential Equations, PDEs, are real. 

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