Extending current mathematical formulations of multiphase flow to regions of strong inhomogeneity

In particle-laden flows, sprays and bubbly flows, it is commonplace to encounter steep gradients in the average number density and volume fraction at material fronts where the multiphase flow penetrates into the continuous carrier phase. The growth of instabilities at the boundary is of critical importance in many applications and is tied to the growth of fluctuations at the interface. This problem violates the standard separation of scales assumption that underlies current multiphase flow theories. This talk examines the adequacy of three commonly used mathematical formulations—ensemble-averaging, volume-averaging and spatial filtering—to capture this important phenomenon. Extensions to current formulations that are needed to relax the scale separation assumption and properly represent this phenomenon will be presented. Connections to flows involving the clustering of dispersed phase entities, which are also characterized by fluctuations in number and volume fraction, will be established. These new formulations have the capability to represent the full range of multiphase flow phenomena. Implications for existing theories, models and simulations will be highlighted.