In classical models of visco-plastic fluids, these materials do not deform when subjected to a shear stress smaller than a certain value, which is called the yield stress. In this range of applied shear stress, these materials behave as ideal rigid solids. If the shear stress in the fluid exceeds the yield stress then the fluid deforms as a (nonlinearly) viscous fluid and is typically shear thinning since the fluid structure breaks down progressively with shear. Therefore, from both a physical and mathematical perspective, the yield stress threshold effects a fundamental change to the fluid mechanics of the problem. The visco-plastic fluids play a prominent role in many industrial processes, as in the food industry (e.g., dairy products, chocolate confections, pulp suspension), the petroleum industry (drilling mud, cement, waxy crude oil), the biological industry (e.g., mucus and blood clot), the natural phenomena (e.g., flows of slurries, debris and lava), and in various complex printing and coating processes. The proposed course is designed for advanced graduate students as well as postdoctoral researchers across several disciplines (e.g., Mathematics, Physics and Engineering), with the aim of providing them with tools and techniques that are essential in performing research on the flow problems of visco-plastic fluids. Notably, we envision a broad and lively discussion of all the theoretical developments, analytical and computational methodologies, recent experimental methods and existing applications. The followings summarize the broad subtopic breakdown introduced by the course:
- Analysis of classical visco- plastic uid models
The history of classical models, the variational formulation, the general results on existence and uniqueness of weak solutions and the hydrodynamic stability.
- Mathematical modeling of flows of visco-plastic fluids Visco-plastic lubrication theory, free-surface flows, sheets and threads and visco-plastic convection.
- Computing flows of visco-plastic fluids
Finite element discretization scheme, the Augmented Lagrangian and the regularized methods in computing visco-plastic flow problems, adaptive mesh refinement techniques and the fictitious domain methods.
- Rheology of visco-plastic fluids and visco-plastic suspensions
Introduction to the conventional Rheometry and recent measuring techniques such as Magnetic Resonance Imaging (MRI) and X-ray microtomography, sedimentation and migration of solid and bubble inclusions.
- Application of visco-plastic fluids in engineering sciences
Flow and shape generation (e.g. forming and extrusion, wall slip, etc.), flow and heat transfer (e.g. casting and fouling) and unsteady ows (e.g. injection moulding, start-up and shutdown, flushing and cleaning).
- Complex flows of visco-plastic fluids
Multi-layer flows of visco-plastic fluids, solid dispersion in flows of visco-plastic fluids, natural phenomena of visco-plastic fluids e.g., submarine avalanches and mudslides.