Rheology of Materials


At the end of this course the student should have acquired knowledge, skills and competence to: recognize the importance of viscoelasticity and how it affects the deformation of the fluid when subjected to shear and extensional stresses; know which parameters affect the rheological functions of the fluids, in particular polymers; understand the rheological behavior of materials and products such as multiphase systems (suspensions, emulsions, polymer blends), cosmetics, food, paints, etc.; measuring rheological properties of different types of fluids, in particular polymers, using appropriate equipment; calculating rheological functions measured  with different geometries; apply the knowledge of the rheological behavior to polymer processing conditions and adjust the results of experimental data to equations / models appropriate and from there to extract relevant information

General characterization





Responsible teacher

Maria Teresa Varanda Cidade


Weekly - 5

Total - 70

Teaching language



There are no mandatory prior courses, however it is advisable that students have knowledge of polymers (acquired in course units of Polymer Chemistry and Physics of Polymers) and mathematics (eg solving differential equations) and fluid mechanics.


H.A. Barnes, J.F. Hutton and K. Walters, “An Introduction to Rheology”, Elsevier Publishers, 1989.

R.B. Bird, R.C. Armstrong and O. Hassager, “Dynamics of Polymeric Liquids: Volume II, Fluid Mechanics”, John Wiley & Sons Inc., 1977.

L.E. Nielsen, “Polymer Rheology”, Marcel Dekker, Inc., 1977.

“Reologia e suas Aplicações Industriais”, A. Gomes de Castro, J.A. Covas e A. Correia Diogo (Eds), Ciência e Técnica (Instituto Piaget), 2001.

“NL Rheology Handbook”, NL Industries, Inc..

 “Paints, Coatings and Solvents”, D. Stoye andW. Freitag(Eds), Wiley – VCH, 2001.

“Introduction to Paint Chemistry and principles of paint technology”, J. Bentley and G.P. Turner, Chapman & Hall, 2000.

“Reologia de Polímeros – Texto de Apoio”, M.T.Cidade, 2005.

Teaching method

With regard to the theoretical contents, exposure of matter will be taken resourting to data show. The slides will be made available to students on the course page. This page will contain all elements relating to the discipline: objectives, program content, scheduling of different types of classes, methods of assessment, problems, scripts of practical work, methods and assessment results, recommended bibliography and summaries.

Concerning problems, students will be asked to solve them previously, the classes serving for correction and clarification of doubts. At the end of the classes of problems, all students, whether they have done, or not, prior resolution of the proposed exercises, will be aware of the resolution, which will be made in the chalkboard, whenever possible by the students themselves.

For practical content, 5  laboratory classes will be given which not only will help students to consolidate the theoretical background but will also familiarize the students with equipments usually used for rheological characterization.

Evaluation method

The evaluation of laboratory work will be done by conducting an individual questionnaire, to be performed one to two weeks after the completion of it.

The final grade (NF) of the subject will be calculated by the expression:


  NF = 0.60 NT + 0.40 NL            (1)



NT - average of the 2 tests performed during the semester, or exam grade

NL - Average of the questionnaires


Students may waive the exam if they have obtained NF equal to or greater than 9.5 val, with a minimum of 8 val in the 1st test, and with NT (grade of attendance) equal to or greater than 9.5 val.

Students who have not successfully passed tests may take an exam as long as they have passed the course.

Subject matter

Chapter 1. Introduction: The concept of rheology and the importance of its study.

Rheology foundations: flow geometry, Hooke''s law, Newton''s law, equations of motion, Navier Stokes equations.

Viscoelasticity: the concept of viscoelasticity, viscoelastic solids and liquids, Déborah number.

Fluid Classification: Newtonian and non-Newtonian fluids (shear thinning, shear thickening, etc.).


Chapter 2. Rheological Functions of Non-Newtonian Fluids. Viscosity: Flow curves, constitutive equations, and models that describe the behavior of non-Newtonian fluids.

Normal stress differences: origin, first normal stress difference as a measure of the elasticity of a fluid, consequences of non-zero normal stress differences.

Linear viscoelasticity: behavior of viscoelastic fluids in linear viscoelasticity regime; complex viscosity, dynamic module and dissipative module.

Extensional Viscosity: types of extensional deformation, importance of extensional flow, relationships between shear and extensional rheological functions.


Chapter 3. Rheological function measuring instruments Simple equipment for routine control.

Rotational rheometers.

Capillary rheometers.

Extensional rheometers.


Chapter 4. Polymer rheology: factors that affect the rheological properties of polymers

Temperature effect. Master curves.

Pressure effect.

Effect of average molecular mass and distribution of average molecular masses.

Effect of molecular structure: effect of branches, effect of other structural factors.

Effect of the presence of additives.

Effect of solvent addition: rheology of polymer solutions; viscosity as a function of concentration, viscosity dependence of polymer solutions with temperature and shear rate, dynamic rheological properties of polymer solutions.


Chapter 5. Rheology of liquid crystalline polymers. Introduction: the notion of liquid crystal and liquid crystalline polymer.

Rheology of lyotropic liquid-crystalline polymers: viscosity curves as a function of concentration, viscosity and normal stress differences as a function of shear rate, influence of temperature, concentration and average molecular weight of the polymer on the rheological functions of lyotropic solutions.

Rheology of thermotropic liquid-crystalline polymers: viscosity and normal stress differences as a function of shear rate, influence of temperature and average molecular weight of the polymer on the rheological functions of thermotropic polymers.

Models applicable to the rheological behavior of liquid crystalline polymers.


Chapter 6. Rheology of multiphase polymer systems Suspension rheology: diluted suspensions, concentrated suspensions,

Emulsion rheology.

Rheology of fiber reinforced polymers.

Rheology of polymer blends. Particular case of the rheology of thermoplastic mixtures with liquid crystalline polymers.

Block copolymer rheology.


Chapter 7. Food rheology

Seminar given by external teacher


Chapter 8. Rheology of Pharmaceuticals and Cosmetics

Seminar given by external teacher


Chapter 9. Ink Rheology

Importance of rheology in the paint industry. Thixotropy and viscosity recovery time.

Factors on which a paint''s rheology depends: nature of the binder, solvent composition, binder concentration, pigment content, temperature.

Relationship between shear rate and paint properties: leveling, sedimentation, painting, etc.

Use of paint rheology modifying additives.

Relationship between paint viscosity and application method.


Chapter 10. Building Materials'' Rheology

Importance of rheology in civil construction and public works. The concepts of yield stress and plastic viscosity and its dependence on the shear rate, temperature and composition of the mixture. Models applicable to the rheology of these materials.

Seminar given by a teacher from DEC.


Programs where the course is taught: