Instructions for doing the project:

Each group of two persons should prepare a 45 minute lecture on their topic.

Each group should also prepare a 1-2 page summary, which is to be handed out to all participants at the presentation. These summaries are to be part of the course material and I will ask questions on their content at the oral exam.

Make sure to discuss your project with me (Gustav Amberg) well before your presentation.The ideal situation is to have a first discussion 1-2 weeks before the presentation, when you have had a first look at the material. We can then sort out any questions you may have, and together decide what to focus on and plan the presentation. If needed we can discuss more later.

Suggested topics: These may change depending on your interests.

Describe the basic rheological properties of suspensions of particles. For instance: What different interactions are there between particles in the suspension, and what is the importance for the rheology? What is a ‘colloidal’ suspension?, etc.

Litterature: Chapter 7 in Barnes, Hutton, Walters + references therein.

Gunnar Maxe, Arnim Brüger

Explain how the shear thinning and/or shear thickening of suspensions can be understood in terms of the local configuration of the suspended particles. Show some of the experimental and theoretical evidence.

Litterature: Richard L. Hoffman, ‘Explanations for the cause of shear thickening in concentrated colloidal suspensions’, Journal of Rheology, 42, pp. 111-123,
Gray and Bonnecaze, Journal of Rheology, 42, pp1121-1151, 1998.
+ references in there.

Mattias Chevalier, Jan Pralits

Suspensions of slender fibres may exhibit large extensional viscosities. There is a theory for such suspensions which captures the essence: explain this. This may have application to rheology of paper pulp.

Litterature: Batchelor , G.K., 1970, 'The stress system in a suspension of force-free particles', J.Fluid Mech. 41, 545-570
Batchelor , G.K., 1970, 'Slender body theory for particles of arbitrary cross-section in Stokes flow', J.Fluid Mech. 44, 419-440
Batchelor , G.K., 1971, 'The stress generated in a non-dilute suspension of elongated particles by pure straining motion', J.Fluid Mech. 44, 813-829
Yamamoto & Matsuoka, ‘Dynamic simulation of fiber suspensions in shear flow’, The Journal of Chemical Physics, 102, pp2254-2260.

Richard Holm, Claes Holmqvist

When a NNf flows through a contraction vortices may appear upstream of the contraction. This flow case is used as a common test case for models. Explain the phenomenon.

Litterature: Boger, D.V., Ann. Rev. Fl. Mech. 19 (1987) p 157, + references therein.

Torbjörn Nielsen, Ulrike Windecker

A small addition of polymers may affect the turbulence in a boundary layer so that drag is reduced. Explain this! In particular show something of how the possibility to do direct numerical simulation of turbulence is helping to prove/disprove older theories.

Literature: Berman, N.S., 'Drag reduction by Polymers', Ann. Rev. Fl. Mech. 1978, 10, p 47.
(SC and JR and references).
Sureshkumar et. al. ‘Direct numerical simulation of the turbulent channel flow of a polymer solution’, Physics of Fluids, 9, pp. 743-755, 1997.

Gustav Mårtensson, François Gurniki

Jun Shiomi, Kristian Angele

The stresses in the fluid must satisfy certain conditions for the mathematical problem to be well posed. It is important to make sure for instance that a numerical simulation does not violate these locally. Explain what the requirements are and where they come from.

Litterature: Ch 4 + more in Joseph, D.D., 'Fluid Dynamics of Viscoelastic Liquids', Springer 1990, ISBN 0-387-97155-6

Mats Larsson, Jens Fransson

Study a detailed comparison between different rheological models for contraction flows.

Litterature: Debbaut, Marchal & Crochet (1988), 'Numerical simulation of highly visoelastic flows through an abrupt contraction', Journal of Non-Newtonian Fluid mechanics, v29.

Azaiez, Guenette & Ait-Kadi, (1996), 'Numerical simulation of viscoelastic flows through a planar contraction', Journal of Non-Newtonian Fluid mechanics, 62., p253-277.
Boger, D.V. (1987), Ann. Rev. Fl. Mech. 19 p 157

Nulifer Ipek, Jerome Ferrari

The mathematical character of the model equations can change from elliptic to hyperbolic, depending on the flow. This is analogous to transsonic flow in compressible fluids, there is a 'visoelastic Mach number'. Explain the basic mathematical considerations and their consequences.

Litterature: Ch 5, and some of ch 6 in Joseph, D.D., 'Fluid Dynamics of Viscoelastic Liquids', Springer 1990, ISBN 0-387-97155-6. References from this book.

François Hillion

When a viscoelastic fluid leaves a pipe in the form of a jet, there is usually some die swell, i.e. the jet expands. If the flow velocity is larger than an appropriately defined wave speed in the fluid, this die swell is delayed, loosely speaking it takes a little while before the jet discovers that it has left the pipe. This is related to a change of type of the mathematical problem from elliptic to hyperbolic. Explain the phenomenon.

Literature: Ch 13 in Joseph, D.D., 'Fluid Dynamics of Viscoelastic Liquids', Springer 1990, ISBN 0-387-97155-6. References from this book.

Christophe Duwig, Luca Brandt

Take a look at what kind of numerical methods are needed to simulate visoelastic flows. The papers listed below describe FEM schemes.

Literature: Szady et.al. 'A new mixed finite element method for visoelastic flows governed by differential contitutive equations', J. Non-Newtonian Fluid Mech. (1995), 59, p215-243. + references therein.
Tanner & Jin, 'A study of some numerical viscoelastic schemes', J. Non-Newtonian Fluid Mech. (1991), 41, p171-196.
Marchal & Crochet, 'A new mixed finite element for calculating viscoelastic flow', J. Non-Newtonian Fluid Mech. (1987), 26, p77-114.

Franck Gregoire, Olga Tchernycheva

Explore the Non-Newtonian capabilities in CFX, and possibly in POLYFLOW.

Use our homemade viscoelastic code to compute some flows, compare some different models.

Johan Gullman-Strand, Jan Östlund.