PHYS0090-1 : Complex fluids and non-Newtonian flows

University of Liege | Version française

Study programmes 2012-2013

Last update : 18/06/2013

PHYS0090-1

Complex fluids and non-Newtonian flows

Duration :

30h Th, 30h Pr

Number of credits :

Master in Engineering Physics, in-depth approach, 2nd year		5

Lecturer :

Vincent Terrapon

Language(s) of instruction :

English language

Organisation and examination :

Teaching in the first semester, review in January

Course contents :

This course is an introduction into complex fluides and non-Newtonian flows.
Many fluids in engineering and industrial applications are complex mixtures. Hence, they 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.
The course is divided in two 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 lead to the 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

Learning outcomes of the course :

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

Know the major types of complexe 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

Prerequisites and co-requisites/ Recommended optional programme components :

Basic knowledge in fluid mechanics (viscous flows, dimensional analysis, ...), and in basic mathematics (tensor algebra, ...)

Planned learning activities and teaching methods :

The theory is illustrated through regular exercises and a small project.
Exercises have the purpose to consolidate the material seen in class. They are therefore graded.
A small project at the end of the course gives the students the opportunity to extend or consolidate the theory seen in class. The 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 small computer code to simulate a specific model or an interesting phenomenon. The exact topic will be discussed with the instructor.
The project will be graded based on a written report and an oral presentation.

Mode of delivery (face-to-face ; distance-learning) :

The course is normally given in class. Exercises and project are done individually and independently by the students.
However, if the number of students taking the class is low, the course will have the form of a self-study based on the course reader. In this case, a meeting with the instructor will take place each week to discuss the theory and homework, and to answer questions regarding the course.