Duration
26h Th, 26h Pr
Number of credits
| Master of Science (MSc) in Engineering Physics | 5 crédits |
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
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
- 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
Learning outcomes of the learning unit
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
Prerequisite knowledge and skills
To efficiently follow this course, it is preferable to have some basic knowledge in fluid mechanics (viscous flows, dimensional analysis, ...), and in basic mathematics (tensor algebra, ...).
Planned learning activities and teaching methods
The course is divided in 11 chapters, covering the entire theory.
Learning activities include four homework (during the first weeks of the quadrimester) to be solved individually at home and to be returned one week later. 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 will 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 will be presented during the first lecture et distributed electronically to all registered students.
Mode of delivery (face-to-face ; distance-learning)
The course is organized as a self-study based on the course reader. This means that the students are expected each week to individually read and learn the corresponding theory in the course reader. A weekly meeting with the instructor will be planned to discuss the theory and homework, and to answer questions regarding the course. The exact schedule of this meeting will be discussed with the studends and the instructor at the beginning of the quadrimester.
The exercises and project are done individually and independently by the students.
Recommended or required readings
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
Assessment methods and criteria
The final grade for the course is based on
- Homework exercises: 30%
- Project (written report and oral presentation): 70%
Work placement(s)
Organizational remarks
The course is taught in English.
The exact schedule and important deadlines are communicated during the first lecture.
Contacts
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 ULg addresses (xxx@student.uliege.be).
- Follow the elementary rules of politeness.