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.