PhD Courses in Denmark

To introduce the participants to rheology of complex fluids, in particular polymeric liquids and suspensions. The participants will learn how to characterise complex fluids and understand their flow behaviour.

A student who has met the objectives of the course will be able to:

• express vectors and tensors in component form in relevant orthogonal co-ordinate systems and explain the principles in non-orthogonal co-ordinate systems.
• analyse simple flow problems with the generalised Newtonian fluid model.
• use the lubrication approximation to simplify 2D and 3D flow problems and explain the conditions for use.
• explain the importance of homogeneous flows such as shear and elongation for measuring stress components and express the stress tensor in these flows.
• explain the analysis and the necessary assumptions for the common measurement geometries: Cone/plate, plate/plate, capillary and elongation (uniaxial and biaxial).
• explain the basic principles of the linear viscoelastic fluid and the domain of validity.
• determine a spectrum of relaxation times from experimental data for polymeric liquids.
• use the time-temperature superposition principle to analyse experimental data for polymeric liquids.
• explain the basic principles of simple rheological models for suspensions and emulsions.
• explain the basic theory of non-linear models for viscoelasticity: differential and integral constitutive equations and micro-mechanical models.
• explain the basic theory of optical birefringence and its use for measuring rheological and structural parameters.
• apply different numerical techniques for simulation of non-Newtonian flows.

The course will contain the following main topics: 1. Introductory fluid mechanics: Equations of change on the basis of fluxes. Equations of change with transport properties. Solution of isothermal and nonisothermal flow problems. 2. Rheology of non-Newtonian fluids. Measurements and material functions. 3. Simple and advanced models for polymeric fluids: the generalized Newtonian fluids, linear viscoelasticity, nonlinear viscoelasticity. Simple models for suspensions and emulsions. 4. Solution of flow problems: Rheometry, extrusion, formation of fibres and film, injection moulding, heat treatment of foodstuffs etc. 5. Analysis of experimental measurements. Classical methods: Steady and oscillatory shear flow. New Methods: Transient elongation. 6. Introduction to optical birefringence.