Module Notes
Module Details
Help students get familiar with:
1. the underlying concepts and flow phenomena commonly associated with polymeric fluids, and how we model these phenomena using mathematical relationships that allow us to calculate the stresses in the fluid, given the flow history
2. techniques commonly used for the experimental characterization of the rheological response of polymeric fluids using simple (model) flows (simple shear flow, extensional flows, mixed flows) and measuring the corresponding material functions: shear relaxation modulus G(t), shear or extensional viscosity, first and second normal stress difference, storage (G') and loss (G") moduli, etc.
3. the art of the constitutive modeling for polymeric fluids (complex fluids with a rich internal microstructure): phenomenological constitutive equations (integral and differential), popular molecular models (Rouse, Ζimm, Reptation).
The student will learn how to describe the complex rheological behavior of polymeric fluids using integral or differential mathematical equations, how to solve these equations for simple flows to get predictions for the relevant material functions, how to test these predictions against experiemental evidence and available rheological data, and how to improve the corresponding mathematical model at the expense (however) of adding complexity to the mathematical relationship.
In the case of the molecular models, the student will learn how to link important molecular parameters (e.g., molecular weight) and physical quantities (e.g., solvent quality, temperature) with the transport properties of polymeric fluids (zero shear rate viscosity, rotational and translational diffusion coefficients, spectrum of relaxation times, shear relaxation modulus, plateau modulus, etc.).
1. An introductory course on transport phenomena (e.g., fluid mechanics)
2. An introductory course on vector and tensor calculus
- Vector and tensor calculus (quick overview) and application in rheology
- Stress tensor and its physical meaning
- Newtonian behavior. Generalized Newtonian behavior
- Non-Newtonian behavior (and demonstration via experiments). Introduction to viscoelasticity of polymer liquids
- Material functions in simple flows: shear viscosity, normal stress coefficients, extensional viscosity, storage and loss moduli, compliance, etc. Trouton’s rule
- The first (phenomenological) viscoelastic models. Maxwell, Voigt and Jeffreys models. The generalized linear viscoelastic model
- Applications of the generalized linear viscoelastic model to the following rheological experiments: start-up of shear flow, stress relaxation after a sudden shearing displacement, stress growth, constrained recoil, small amplitude oscillatory shear flow, creep. Calculation of the corresponding material functions
- Fitting linear viscoelastic data. The relaxation spectrum. Time-temperature superposition principle
- Other viscoelastic models (continuum models): Οldroyd-B, Giesekus, Phan-Thien/Tanner (PTT). Comparison of the viscoelastic models
- Introduction to molecular theories of polymers: Rouse model and normal mode analysis, tube model and reptation theory
1. R.G. Larson, Constitutive Equations for Polymers Melts and Solutions (Butterworths Series in Chemical Engineering, 1988).
2. R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids; Vol. 1, Fluid Mechanics, 2nd Ed. (John Wiley & Sons, New York, 1987).
3. R.B. Bird, C. F. Curtiss, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids; Vol. 2, Kinetic Theory, 2nd Ed. (John Wiley & Sons, New York, 1987).
The instructor prefers teaching by writing a lot on the board but also by using videos to demonstrate the key properties of flowing polymer fluids and the concepts used to describe these properties.
Related problems are also solved on the board. Emphasis is given to old exams as a method for preparing the students for the final exam at the end of the course.
Typically, the students have about one week to solve the problems themselves (they can also ask for advice or help from the instructor) before these are fully solved in the class.
1. Weekly (or biweekly) homework sets (optional)
2. Final written exam