Abstract Fluid dynamic equations are used to model various phenomena arising from physics, engineering, astrophysics, geophysics. One feature is that they take place at different time and length scales it important understand which occur according the use of single or interactions them. From a mathematical point view, these physical behaviours give rise singular limits and, consequently analysi...

Eulerian-Eulerian computational fluid dynamic (CFD) models allow the prediction of complex and large-scale industrial multiphase gas–liquid bubbly flows with a relatively limited load. However, interfacial transfer processes are entirely modelled, closure relations that often dictate accuracy entire model. Numerous sets closures have been developed, optimized over few experimental data achievin...