Complex fluids - such as polymer solutions, colloidal suspensions, worm-like micelles, and gels - are ubiquitous in industrial, biological, and environmental systems. Their behaviour often deviates from Newtonian fluids due to their intricate microstructure, exhibiting viscoelasticity, yield stress, shear thinning/thickening, and thixotropy. Understanding and predicting their flow dynamics requires advanced theoretical and numerical tools that extend beyond the scope of classical fluid mechanics.

This course aims to provide a comprehensive introduction to the continuum modelling of complex fluids, bridging the gap between theoretical foundations and practical applications. It is designed for doctoral students, postdoctoral researchers, and early-career scientists in engineering, physics, and applied mathematics with a solid background in fluid mechanics or rheology.

Participants will be introduced to the principles underpinning the rheology of non-Newtonian materials, the derivation and application of constitutive models, and modern analytical and computational tools for predicting their flow behaviour. The course will combine fundamental theory with practical examples drawn from research and industry, highlighting the relevance of continuum models in solving real-world problems.

The course offers:
• A solid foundation in the modelling and numerical simulation of non-Newtonian fluids.
• Key concepts such as lubrication theory, linear and nonlinear stability analysis, and advanced constitutive modelling (e.g. viscoelastic, viscoplastic, and elastoviscoplastic models).
• Insight into experimental correlations, model validation, and the challenges of parameter estimation in complex rheological systems.
• Exposure to state-of-the-art research and applications in both academic and industrial contexts.

Course Format
The school begins with four shared introductory lectures to establish a common background. These lectures are essential to ensure that all participants, who are expected to come from a wide range of scientific and engineering disciplines, start from a shared baseline of knowledge. The sessions will review key principles of fluid mechanics and rheology and introduce the basic ideas of continuum modelling before moving on to specialised topics.

This is followed by thematic lectures from six international experts, each focusing on a specific research area. Topics include generalised Newtonian fluids, viscoelastic and yield-stress models, constitutive parameter estimation, stability theory, finite element modelling, and flow classification methods.

Participants will also engage in:
• A flash poster presentation (Day 1 afternoon) for a brief introduction to participants’ research topics.
• A poster session following the flash presentations, promoting informal discussion and collaboration.
• Daily interactions and collaborative learning sessions.

Target Audience
• Doctoral students and young researchers starting in the field of complex fluids.
• Experimentalists aiming to strengthen their theoretical and modelling expertise.
• Engineers, applied physicists, and mathematicians with a strong technical background.
• Industrial practitioners interested in modern modelling approaches for non-Newtonian materials.

The course equips participants with the conceptual and computational tools needed to critically assess, apply, and extend existing models for complex fluids, enhancing their ability to tackle research and engineering challenges in the field.