2023-2024 / PHYS3133-1

Complex fluids and non-Newtonian flows


26h Th, 26h Pr

Nombre de crédits

 Master : ingénieur civil physicien, à finalité5 crédits 


Vincent Terrapon

Langue(s) de l'unité d'enseignement

Langue anglaise

Organisation et évaluation

Enseignement au premier quadrimestre, examen en janvier


Horaire en ligne

Unités d'enseignement prérequises et corequises

Les unités prérequises ou corequises sont présentées au sein de chaque programme

Contenus de l'unité d'enseignement

Many fluids in engineering and industrial applications are complex mixtures. Hence, they often demonstrate a non-Newtonian behavior in the sense that the stress endured by a macroscopic fluid element is not a linear function of the shear rate. In particular, their viscosity can depend on time, or on stress. These rheological properties are induced by changes in the complex microstructure of these fluids under stress and can have a profound impact on the macroscopic flow characteristics.

The objective of the course is to illustrate some of these effects, to demonstrate the relation between the microstructure changes under shear and the macroscopic rheological properties, and to introduce some of the models and analysis tools used in practice.

After a review of basic concepts, the course is divided in two main parts.

The first part covers the macroscopic description of rheology. This includes following topics:

  • Types of complex liquids (colloidal and non-colloidal suspensions, solutions, melts, ...)
  • Macroscopic behaviors (shear-thinning, shear-thickening, time-dependence, ...)
  • Linear viscoelasticity: models in integral and differential forms (Maxwell, Jeffrey), memory function, relaxation modulus, storage and loss moduli, complex viscosity
  • Nonlinear viscoelasticity: models in integral and differential forms (convected Maxwell, convected Jeffrey, convected generalized Maxwell), other constitutive models, examples of simple flows

The second part focuses on the microscopic description of rheology. The main goal is to highlight how the microscopic dynamics of these complex fluids leads to their macroscopic behaviors. It includes following topics:

  • Suspensions of dilute non-Brownian spheres and the concept of stresslet
  • Non-colloidal dilute suspensions of fibers and the concept of conservation of probability, slender body theory
  • Brownian motion and Fokker-Planck equation, Brownian stress and torque
  • Linear viscoelastic behavior of Brownian rod suspensions and calculation of macroscopic rheological properties
  • Dilute polymer solutions, Hookean and nonlinear dumbbells, constitutive equations, models with internal modes of relaxation

Acquis d'apprentissage (objectifs d'apprentissage) de l'unité d'enseignement

At the end of the course, the students should be able to:

  • Know the major types of complex fluids
  • Understand the macroscopic behaviors of non-Newtonian flows
  • Explain the differences between linear and nonlinear viscoelasticity
  • Understand the effect of Brownian motion
  • Explain the link between the microscopic dynamics and the macroscopic behavior
  • Explain the influence of the key parameters on the rheological properties of the fluid
  • Derive constitutive equations from micro- or mesoscopic models
  • Apply linear viscoelasticity to analyze the behavior of complex fluids
  • Use macroscopic constitutive equations in numerical simulations of non-Newtonian flows
  • Read and understand scientific papers from the literature on the subject
This course contributes to the learning outcomes I.1, I.2, II.1, II.2, III.1, III.2, III.2, III.3, III.3, IV.1, VI.1, VI.2, VII.2, VII.3, VII.4, VII.5 of the MSc in engineering physics.

Savoirs et compétences prérequis

To efficiently follow this course, it is preferable to have some basic knowledge in fluid mechanics (viscous flows, dimensional analysis, ...), and in fundamental mathematics (tensor algebra, ...).

Activités d'apprentissage prévues et méthodes d'enseignement

The course is divided in 11 chapters, covering the entire theory. 

Learning activities include 4 homework (during the first weeks of the quadrimester) to be solved individually at home and to be uploaded on gradescope. These homework are evaluated and count towards the final grade. Their objective is to ensure a continuous learning of the subject, to consolidate the material seen in class, to allow a self-evaluation for the students, and to help the instructors in identifying the difficulties encounted by the students. 

Finally, a small project at the end of the course gives the students the opportunity to extend or apply the theory. This project consists either in analyzing one or more papers from the literature on a subject not directly covered in the course, or in developing a computer code to simulate a specific model or an interesting phenomenon. The exact topic should be discussed with the instructor. This project is evaluated based on a written report and an oral presentation.

A detailed calendar of the course and important deadlines is presented during the first lecture et distributed electronically to all registered students.

Mode d'enseignement (présentiel, à distance, hybride)

Cours donné exclusivement en présentiel
Combinaison d'activités d'apprentissage en présentiel et en distanciel

Explications complémentaires:

The course is organized as a self-study based on a detailed course reader. This means that the students are expected each week to individually read and learn the corresponding theory in the course reader.

Additionally, a weekly face-to-face meeting with the instructor is planned to discuss the theory and homework, to answer questions regarding the course material and to introduce the next lecture. 

The course organization is discussed in more details during the first lecture.

Lectures recommandées ou obligatoires et notes de cours

The course material (course reader, problem sets, ...) will be posted weekly on the course website: www.mtfc.uliege.be/Non-Newtonian.

Other useful reading material and reference manuals include:

  • "The Structure and Rheology of Complex Fluids", R.G. Larson
  • "Dynamics of Polymeric Liquids", R.B. Bird, R.C. Armstrong & O. Hassager
  • "Stochastic Processes in Polymeric Fluids", H.C. Oettinger
  • "The Theory of Polymer Dynamics", M. Doi & S.F. Edwards
  • "Non-Newtonian Flow and Applied Rheology", R.P. Chhabra & J.F. Richardson
  • "Advanced Transport Phenomena", G. Leal

Modalités d'évaluation et critères

Travail à rendre - rapport

Evaluation continue

Explications complémentaires:

The final grade for the course is based on

  • Homework exercises: 30%
  • Project (written report and oral presentation): 70%


Remarques organisationnelles et modifications principales apportées au cours

The course is taught in English.

The exact schedule and important deadlines are communicated during the first lecture.

The homework submission relies on gradescope.

Note that, depending on the sanitary situation, the course organization might need to be adapted.

There is no major change with respect to previous year.


Students are encouraged to actively interact with the instructor, also outside of the lectures. It is highly recommended to set up an appointment first. It is expected that the students follow a few basic rules when communicating by email: 

  • Indicate as subject "PHYS3133: ...".
  • Only use ULiege addresses (xxx@student.uliege.be).
  • Follow the elementary rules of politeness.
Prof. Vincent E. TERRAPON; MTFC Research Group; B52, 0/415; +32(0)4 366 9268; vincent.terrapon@uliege.be; http://www.mtfc.uliege.be

Association d'un ou plusieurs MOOCs