Multiphase flows are common in nature and engineering. Atmospheric flows often involve the dispersion of droplets or solid particulate matter (dust, sand, ice crystals in clouds); marine systems are populated by plankton, sediments or microplastics. Industrial applications of disperse flows include particle separators, filtration systems, atomisers and combustion devices, spray dryers, bubble columns; interfacial and free-surface flows are widespread in chemical and process industry.

To address the complexity associated with such flows, diverse phenomena are combined: flow dynamics (including turbulence or microfluidics), transport of dispersed phase, heat transfer and phase change, chemical reactions, surface science (particle deposition, resuspension or agglomeration) or even biology of organic objects. These multiphysics processes may span a wide range of spatial and temporal scales (from nano through macro to geophysical ones).

The course will focus on Lagrangian approaches. They are often methods of choice to treat the particulate phase transport and polydispersity; they may also be used, in terms of so-called particle-based methods, for the macroscopic description of fluid motion. Looked at from this perspective, the course should nicely complement a typical curriculum on fluid dynamics and CFD modelling to provide a broader view, next-to (but not off) the beaten track, especially valuable for PhD candidates.

The course will cover a range of Lagrangian techniques in use, with a special emphasis on particle-laden turbulence. It will include lectures and hands-on sessions on Particle Image Velocimetry and Particle Tracking Velocimetry that are widely used to measure dispersed two-phase flows. On the other hand, non-spherical tracer particles can be used to quantify turbulence. The physics of particle dispersion, aggregate breakup, and anisotropic particle dynamics will be covered.

In terms of modelling and computation, the lectures will describe hybrid Euler-Lagrange approaches for multiphysics two-phase flows, in particular disperse turbulent ones. The course will address particle-resolved and particle-modelled Direct Numerical Simulations (PR-DNS, PM-DNS), Large-Eddy Simulations (LES) with particle tracking, which may include modelling of the subscale phenomena, as well as statistical (RANS and one-point PDF) approaches with stochastic Lagrangian models to account for the missing information on turbulence. Smoothed Particle Hydrodynamics (SPH) will be presented as a representative of a particle-based numerical approach, including multiphase SPH, along with some fundamental issues.

Through these various examples, similarities and differences between particle-based descriptions will be discussed, considering the multiphysics nature of two-phase flows. The lectures will shed light on experimental issues (including uncertainty assessment), modelling challenges (point-particle vs. particle-resolved models, unresolved scales handling), and computational approaches (including hybrid ones).