Paper Number
SG15 

Session
Self-assembled Systems, Gels and Liquid Crystals

Title
Quasi-properties and fractional constitutive equations for protein gels: Connecting gel microstructure to power-law linear rheology

Presentation Date and Time
February 14, 2017 (Tuesday) 10:00

Track / Room
Track 3 / White Ibis

Authors (Click on name to view author profile)

1. Divoux, Thibaut (Centre de Recherche Paul Pascal)
2. Keshavarz, Bavand (MIT, Mechanical Engineering)
3. Leocmach, Mathieu (Université Claude Bernard Lyon 1, Institut Lumière Matière)
4. Gibaud, Thomas (Ecole Normale Supérieure de Lyon, Laboratoire de Physique)
5. Manneville, Sébastien (Ecole Normale Supérieure de Lyon, Laboratoire de Physique)
6. McKinley, Gareth H. (Massachusetts Institute of Technology, Mechanical Engineering)

Author and Affiliation Lines (in printed abstract book)
Thibaut Divoux¹, Bavand Keshavarz², Mathieu Leocmach³, Thomas Gibaud⁴, Sébastien Manneville⁴, and Gareth H. McKinley^2
1Centre de Recherche Paul Pascal, Pessac, France; ²Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; ³Institut Lumière Matière, Université Claude Bernard Lyon 1, Lyon, France; ⁴Laboratoire de Physique, Ecole Normale Supérieure de Lyon, Lyon, France

Speaker / Presenter 
Divoux, Thibaut

Text of Abstract
In the present work we investigate the physical origin of the power-law rheology of model acid-induced protein gels. Viscoelastic soft solids are prepared by mixing sodium caseinate and glucono-delta-lactone (GDL) in water at different concentrations. Once mature, these gels show a robust power-law response in the time/frequency domain to the traditional linear viscoelasticity tests consisting of frequency sweeps, stress relaxation and early creep. A one-element fractional (Scott Blair) model captures this striking behavior and requires only two parameters to describe the linear gel rheology, which are a ‘quasi-property’ or ‘gel strength’ and a dimensionless exponent. To provide a physical interpretation of the latter parameters, we perform two sets of experiments. First, using space- and time-resolved measurements during the gelation we show that such power-law behavior emerges at the gelation point, and that the corresponding fractional exponent decreases towards a terminal value reached when the gel is fully mature. Time lapse images recorded by confocal microscopy reveal that the fractal dimension of the network evolves likewise, which allows us to link quantitatively the fractal properties of the network to the fractional exponents. Second, a thorough characterization of mature gels prepared with different amount of proteins and GDL allow us to directly link the two parameters of the fractional constitutive model to the sample microstructure. Gels prepared with the same GDL/protein ratio show a constant power-law exponent and similar microstructures which allow us to confirm quantitatively the link between the gel fractal dimension and the power-law exponent. Moreover, the gel strength increases with the protein content, which can be interpreted by simple scaling arguments to lead to a fractal dimension consistent with the one determined from the power-law exponent. Our results provide, for the first time, a direct link between a gel microstructure and its resulting power-law rheology.