The term “complex fluids” refers to a broad class of liquids and soft materials with complex microstructure; examples are polymer melts or solutions, gels, colloidal pastes, foams, emulsions, surfactant solutions, slurries, and many others. Depending on their microscopic structure, the macroscopic behaviour of these fluids can exhibit significant differences with respect to simple fluids such as water or air. From the macroscopic point of view of continuum mechanics, their behaviour is usually described using non-Newtonian constitutive models, where the stress tensor is a generic function of the velocity gradient tensor and its derivatives, although in several cases the continuum approach is not sufficient to capture its phenomenology, and molecular models must be used. The recent decades witnessed a fast-growing interest in complex fluids, largely driven by their relevance in a multitude of practical applications, such as painting, advanced manufacturing, food processing, cosmetics and personal care products, and many others. Moreover, with a better understanding of the microscopic structure of complex liquids, industries have realized that working fluids can be tailored specifically to optimize existing industrial processes, by altering their formulation (e.g., by means of chemical additives) in such a way as to change one or more physical properties. An example of industrial optimization is the use of polymer additives in agrochemical formulations, which improves the application efficiency of agrochemical sprays and reduces the environmental impact from ground contamination. In this context, a detailed understanding of the mass, momentum, and energy transport mechanisms in complex fluids is very important and has a significant impact on everyday practical applications.

The aim of this course is to provide a thorough overview of transport phenomena in complex fluids, based on the most recent research results and the most updated methods for their analytical prediction and numerical simulation. Lectures will cover several topics, including: a description the structural features of the most common complex fluids (polymer and surfactant solutions, colloidal suspensions); an introduction to the most common non- Newtonian constitutive models and their relationship with the fluid microstructure; a detailed overview of the experimental methods to characterise the thermophysical properties, the bulk rheology, and the surface properties of complex fluids; a comprehensive introduction to heat, mass, and momentum transport, and to hydrodynamic instabilities in complex fluids; an introduction to state-of-the-art numerical methods to simulate complex fluid flows, with focus on the Smoothed Particle Hydrodynamics (SPH) and the Dissipative Particle Dynamics (DPD) techniques. A number of lectures will be dedicated to an in-depth description of phenomena such as thermal convection, elastic turbulence, mixing of complex fluids, thermophoresis, sedimentation, non-Newtonian drops and sprays. The course is addressed to research scientists and professionals, engineers, R&D managers and graduate students in the fields of Engineering, Chemistry, Biology, Medicine, Applied and Fundamental Sciences. Participants will be given the opportunity to present their own research, and discuss their individual challenges and results with the instructors during a round table at the end of the course.