The purpose of the course is to introduce concepts and methods that are relevant for understanding and model the flow of systems of two or more fluids, and the transport and dynamics of suspensions of e.g. particles and polymers. The course is devoted to students with different backgrounds, and it is aimed to supply fundamental knowledge on multiphase flows and on the different approaches used to for mathematical models and numerical simulations. The subject is inherently linked to several programmes as it also considers mixing and interfacial heat and mass fluxes in geometries of microscopic dimensions as well as in turbulent flows.

The students will learn about the flow and transport in two-fluid systems, about the dynamics of particle suspensions and modulations of turbulence in the presence of additives (particles, bubbles, etc.). The students will be able to recognize the different regimes associated to droplet/bubble deformation and breakup and choose appropriate models as function of their size, deformability, and number. Similarly, for the case of particle and sediment transport. Student will learn about the basic heat and mass transfer at an interface and the assumptions behind the different models. The computer lab sessions will introduce the student with different simulation tools for interface tracking and capturing, and particle models, so to consolidate their knowledge and improve their coding skills. The students will develop critical thinking, team working attitude and technical communication skills also thanks to the course project work and final presentation.

Theory and models: Recall of conservation laws for mass, momentum and energy in fluid flows. Flows at high and low Reynolds number (reversibility of flows at the micro scale). Mixing: advection/diffusion. Taylor dispersion and chaotic mixing at microscale. Complex fluids: basic concepts of rheology. Continuum models for viscoelastic and viscoplastic flows (Oldroyd-B, FENE-P…). Two-fluid systems: interface conditions and surface tension. Static and dynamic wetting. Dynamics of droplets and bubbles (deformation, breakup). Turbulent emulsions and bubbly flows. Heat-transfer in multiphase flows. Free-energy and phase change. Particle suspensions. Particle dynamics: transport and settling. Rheology of particle suspensions. Turbulence modulations in particle-laden flows. Basic concepts of electro-hydrodynamics: electro-osmosis, electro-phoresis and dielectrophoresis. Computational models: interface-resolved simulations. Interface tracking and capturing methods for deformable interfaces and rigid particles. Large-scale models: Eulerian-Eulerian and Eulerian-Lagrangian models (Discrete-particle methods) Closure problems for two-fluid models. Example of final project work: Locomotion in the inertialess flows Models for elastic membranes in low-Reynolds number flows (redblood cells, capsules, vesicles) Elastic instabilities in microscale flows Role of surfactants: chemical engine in microfluidics Inertial microfluidics Heat transfer in bubbly flows Heat transfer and thermal convection below melting ice CO2 absorption/desorption: gas transfer and chemical reactions Inertial particles in turbulent flows: turbophoresis Two-fluid models for sediment transport Diffuse-interface approaches for phase change Models for the numerical simulations of inertial particles in vortical flows

The course is 60 hours long and it is organised as follows. 52 hours are dedicated to lectures about fundamental and technical knowledge. During the lectures, students are often involved with questions and exercises, discussed within the whole class to assess the comprehension of principles and theory. 8 hours are dedicated to computer lab when students will be introduced to numerical tools for multiphase flows with the supervision of the professor and/or an expert assistant. This activity has the objective of developing technical competence and deepening the understanding of tools currently used in industry and research. At the final exam, students should present a numerical or literature-based study. Individually or in groups of 2, students further deepen a topic of own interest (also depending on the specific programme they are enrolled in) and discuss relevant industrial applications or modelling aspects.

Basic fluid mechanics book (e.g., Fluid Mechanics by P.K. Kundu & I.M. Cohen) Introduction to Microfluidics, Tabeling, P., Oxford University Press. Theoretical Microfluidics, Bruus, H., Oxford University Press. Material available on the web (portale della didattica): lecture slides, limited portions of reference books; scientific papers (tutorial and basic papers) as further readings

Modalità di esame: Prova orale obbligatoria; Elaborato progettuale individuale;

Exam: Compulsory oral exam; Individual project;

... the oral exam will be defined at the exam date. The exam consists in questions and exercises of the same kind of those normally solved in class. The oral exam will be divided in 3 parts: 1) Project presentation and discussion. 2) Questions on basic definitions and concepts. 3) Open questions about relevant applications. The exam duration is about 30-40 minutes. The final mark is composed as follows: max 27 points for part 1) and 2), from -3 to + 6 for final open discussion. Rules during oral exams: the exam is closed book.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.