A statistical model for the average volume fraction profile through the mixing zone in turbulent stratified gas–liquid flow

• A new statistical model was developed for the volume fraction through the mixing zone between stratified, turbulent fluids.
• An interfacial probability distribution was defined in terms of the interfacial energy and the turbulent kinetic energy.
• The model offers an alternative boundary condition for dispersion models.
• An interfacial roughness can be extracted from the model.

A phenomenological model was developed for the average volume fraction profile through the mixing zone between turbulent gas and liquid in horizontal, layered flow. A probability distribution (PDF) of the height of the interface was defined in terms of a ratio between the interfacial energy (system energy) and the turbulent kinetic energy (driving energy), representing an analogy to the Boltzmann distribution in statistical physics. A potential advantage with this modelling approach is that it offers an alternative to (often inaccurate) entrainment correlations that are used in boundary conditions for dispersion models. A unified PDF and dispersion model was tested against X-ray tomography data, with satisfactory results.