This two-week summer school is aimed at young researchers who want to develop their ability to model and analyse the behaviour of simple and complex fluids in confined evolving geometries; particularly, when the dynamics of bulk liquids and interfaces are coupled. The summer school will also allow experts to formulate and discuss fundamental questions of the field. The school will emphasise useful mathematical approaches of modelling, analysis and simulation, and will facilitate the transfer of knowledge between the various interested scientific communities. A number of Problem Sessions will highlight open challenges in the field.
Subjects to be treated include descriptions of the bulk behaviour of complex liquids as mixtures, solutions, suspensions, liquid crystals, morphactants, swimmers and active colloids. This equally features an introduction to the geometric approach to modelling complex fluids as a hydrodynamic theory of flocking. In parallel to the bulk descriptions, boundary effects and evolution will be discussed, e.g., capillarity and wetting effects for simple liquids, mixtures and liquid crystals, etc. Some attention will also be paid to the motion of a three phase contact line for simple and complex liquids and to gradient dynamics formulations of evolution equations for free surface films. The relations of the various models to equilibrium and non-equilibrium thermodynamics will be stressed.
The lectures will introduce various model types and derivation strategies as well as methods for their analysis and simulation. Examples include: Lattice Boltzmann Methods for complex fluids; particle-based scheme for cells and vesicles; phase field and other PDE methods; geometric mechanics of fluids; long-wave expansions and other asymptotic methods; linear techniques; dynamical renormalisation groups; the usage of methods from dynamical systems theory and pattern formation to understand, e.g., the role of localised states in fluid motion and phase transitions.