Two-phase flows are common in environmental and industrial applications. To name a few examples, dispersion of solid & liquid matter in atmospheric flows (dust, sand, droplets or ice crystals) or marine systems populated by a number of organic & inorganic objects (e.g., plankton, sediments, or microplastics). Two-phase flows are also a matter of concern in industrial systems (e.g., spray dryers, bubble columns, combustion engines) which can involve complex fluids (e.g., containing polymers or colloids) as well as interfacial and free-surface flows.

To address the complexity of these phenomena, models require to combine a range of disciplines such as fluid dynamics (including turbulence or microfluidics), transport of a dispersed phase, surface science, thermodynamics & chemistry (including phase changes), soft matter physics (e.g. predicting materials properties or transport coefficients) or even biology. A specific challenge is that these processes span a wide range of spatial and temporal scales (from nanometers/nanoseconds to kilometers/days).

The aim of this course is to explore multiphysics and multiscale aspects of two-phase flows through particle tracking methods. Whereas handling fields is natural in areas pertaining to continuum mechanics, Lagrangian approaches have been gaining increased attention in past decades. In fact, for dispersed two-phase flows, they allow to treat without approximation key phenomena (like transport or polydispersity) and are flexible enough to include specific models (like thermal noise for fluctuating hydrodynamics). Moreover, they constitute an adequate framework in which models at the mesoscopic and macroscopic levels of description can be naturally coupled, providing a consistent methodology throughout these scales.

The course is organized so as to cover a range of available Lagrangian techniques. This will include lectures on particle tracking measurement principles and methods (e.g., PIV & PTV). On the micro- and mesoscopic levels, lectures on modeling approaches encompass methods used in statistical physics (typically below the hydrodynamic level, such as Dissipative Particle Dynamics (DPD) or Smoothed Dissipative Particle Dynamics (SDPD))for the dynamics of molecules/super-molecules). On the macroscopic level, meshfree and particle methods used in computational fluid dynamics for single- and multi-phase flows will be presented (like Smoothed Particle Hydrodynamics (SPH)). Concerning turbulent particle-laden flows, lectures will cover Direct Numerical Simulations of turbulent flows coupled to detailed DEM tracking approaches, alongside spatially-filtered approaches (Large-Eddy Simulations with sub-scale models for particle dynamics) and all the way up to macroscopic stochastic PDF approaches based on mean-field theories.

Through these various examples, similarities and differences between particle-based descriptions will be highlighted. The lectures will shed light on experimental issues (e.g., uncertainties), modeling issues (how to select key factors in a physical description of a system, how to model unresolved scales), and computational issues (like consistency and compatibility in hybrid approaches).