CISM-EUROMECH Advanced Course on "Fluid Mixing: Fundamentals and Practices"

Fluid mixing or the process of homogenization of gradients of scalar fields such as concentration or temperature is ubiquitous in nature and may be observed over a broad range of spatial scales starting from the microscopic scale (e.g. in porous media or bio-physical flows) up to geophysical flows (e.g. mixing of bio-mass by ocean currents). The relevance of fluid mixing across the disciplines is twofold. From a practical standpoint, understanding the physics of mixing is of paramount importance in optimizing industrial processes that rely on the efficient transport of mass and/or heat related to a variety of modern industrial settings such polymer processing, food engineering, bio-chemical engineering. The control and optimization of practically relevant mixing processes may be achieved various approaches including by either special design of the flow geometry, optimized flow forcing schemes or fine tuning of the rheological properties of the fluids to be mixed. Regardless the approach that is undertaken, a deep physical understanding of the interplay between diffusion and advection in each particular context is needed in order to achieve this goal. From a fundamental standpoint, a systematic understanding of the fluid mixing requires an interdisciplinary effort at the intersection of several disciplines: fluid mechanics, applied mathematics, chaos and nonlinear dynamics, chemical and biological engineering. The central aim of this course is to provide a thorough overview of mixing in various flows based on the most recent research results and most up to date methods used in either experiments or analytical predictions and/or their numerical validation. The course is organized along three blocks. Within the first block, fundamental theoretical aspects on flow kinematics, advection, diffusion, mixing, rheology will be introduced. Through the second block, modern approaches to characterize mixing in chaotic flows including nonlinear dynamics tools, braiding theory, finite size Lyapunov exponents, finite time Lyapunov and quanta. will be detailed. Within the third block, mixing will be discussed in several specific contexts: porous media, geophysical flows, industrial flows and rheologically complex fluids.