Rheology Short Course

The short course is scheduled for April 13th and 14th, featuring two full days of immersive lectures and hands-on data analysis. A buffet lunch and regular coffee breaks will also be provided. Each day will focus on a distinct topic, covering both fondament concepts and the latest developments in the field. This combination of lectures and hands-on practice gives participants a balanced and engaging learning experience.

April 13th 2025 - "Viscoelastic Materials Under External Stimuli"

Instructors:  Prof. Annette M. Schmidt (U. of Cologne, Germany) & Dr. Alain Ponton (UPC-CNRS, France)

   

Stimuli-responsive soft matter is the subject of intensive research and shows a bouquet of prospective applications due to its capability to undergo abrupt property changes, such as two-dimensional or three-dimensional shape changes, under the influence of external stimuli, including pH, temperature, UV/visible light, or electrical or magnetic fields. 

Following an introduction to the concept of soft matter and several illustrative examples of different responsive polymer materials, the course will focus on magneto-sensitive materials, from their initial elaboration to the study of their controllable properties at different scales. In particular, the presentation will discuss experiments and results that demonstrate the correlation between the magnetic, mechanical, and in-situ microstructural properties in synthetic and biopolymer-based gels. The participants will thus have the opportunity to investigate the characteristics of magneto-responsive soft materials, from their fluid to viscoelastic states, and the relationships between their macroscopic properties and microstructure.

 

 

Course Outline: (4 x 1.5 lectures)

Lecture 1

·      Introduction to soft matter 

·      Viscoelasticity and rheological properties

·      Examples of stimuli-responsive materials 

 

Lecture 2 

·       Magnetic fluids

·       magneto-optical-rheology

·       Results on ferrofluids and magnetic hydrogels 

 

Lecture 3

·        Micro- and Nanorheology

·        Diffusivity of small particles in complex media       

·        Magnetic Particle Nanorheology of viscoelastic systems

            

Lecture 4

·       Magnetic manipulation of matter 

·       Magnetoactive soft materials

·       Multifunctional magnetic particles

 


 

 

April 14th 2025 - "Applications of Fractional Calculus to Viscoelasticity"

Instructors:  Dr. Alessandra Bonfanti (Politecnico-Milano- Italy) & Prof. Gareth H. McKinley (MIT-USA)

 

This one-day short course on applications of fractional calculus to viscoelasticity will first review key concepts of linear viscoelasticity, emphasizing the limitations of classical (spring-dashpot) models in capturing the rheological behavior of soft materials, ranging from gels to biological tissues. Traditional linear models often fall short when applied to systems with complex microstructures or broad (power-law) time-dependent responses. To overcome these challenges, the course introduces the concepts of fractional-order derivatives and fractional constitutive models (based on the concept of a “spring-pot” element) which offer a more flexible and accurate framework for accurately modeling many complex fluids as well as soft solid materials such as hydrogels. It then delves into nonlinear differential and integral fractional models, highlighting their capacity to describe the onset of nonlinear (rate- and strain-dependence) in the rheological response of such materials.  These new families of fractional constitutive models provide deeper insights and connections to the underlying fractal or multiscale microstructures of many real-world and multicomponent materials, as well as enhanced predictive capabilities with fewer model parameters, offering significant practical advantages in several scientific fields. Participants will also explore the integration of these advanced constitutive models into machine-learning algorithms using Julia. Finally, the course provides hands-on guidance in fitting experimental rheological data using both traditional and fractional models, with practical sessions supported by the RHEOS (RHEology Open Source) package in Julia.

 

Course Outline: (4 x 1.5 lectures)

Lecture 1

·        Introduction to fractional calculus (motivation/overview)

·        History of the fractional derivative; Scott-Blair

·        Notation; quasi-properties, powerlaw indices

·        Fractional diffusion

·        Connections to classical Maxwell and Kelvin-Voigt Models

·        Compact descriptions of Experimental Data (parsimonious models, extrapolation)

 

Lecture 2

·        Characteristics of traditional models (the generalized relaxation spectrum)

·        From traditional viscoelastic models to fractional ones (and derivation of their constitutive equations)

·        The Mittag-Leffler function (qualitative behaviour and computation)

·        Heuristic overview and hierarchy of Fractional Maxwell and K-V models

 

Lecture 3

•       Pipkin Diagram and Extension to Nonlinear Deformations

•       The Strain Damping Function

•       Fractional K-BKZ formulations; normal stress differences

 

Lecture 4

•       Fitting rheological experimental data using linear viscoelastic models (including classical multimode models and fractional formulations).

•       Introduction to RHEOS (https://github.com/JuliaRheology/RHEOS.jl)  and its structures (data structure and code)

•       Practical training session on RHEOS