Interfacial momentum exchange

The interfacial momentum exchange terms in the momentum conservation equations for each phase consist of drag and virtual mass force terms. The drag force for gas and liquid is modeled, respectively, as 

The second drag coefficient model was proposed by White (1974)  

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Interfacial momentum transfer to phase k Interfacial momentum exchange between phases k and I (kg/m s )... 

The form of Eq. (5.9) models a retum-to-isotropy effect due to fluctuating interfacial momentum coupling and reduces the turbulent viscosity from that predicted by the single-phase model. The turbulence energy exchange rate coefficient Ey is given by... 

In contrast with the mathematical dividing surface, which has an isotropic interfacial tension (7, the forces acting on the material interface are not isotropic. They are characterized by the interfacial stress tensor, a, which is a two-dimensional counterpart of the bulk stress tensor, P. The two-dimensional analogue of the momentum balance equation (1) written in the bulk is called the interfacial momentum balance equation. Note, that the inter-phase exchanges momentum also with the contiguous bulk phases and the corresponding balance equation reads (Slattery 1990, Edwards et al. 1991) ... 

Two-phase flows have all the complexity of single-phase turbulent flow, but in addition, there are now interfaces which have to be considered. Through the interfaces the interfacial tension forces act and the exchange of mass, momentum, and heat between the liquid and gas phases occur. Since the flow conditions in a flow channel vary along its length, over its cross section, and with time, the gas-liquid two-phase flow is an extremely complex three-dimensional (3D) transient problem. Often simplified descriptions of the... 

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