Acid-induced protein gels: from gelation to stress-induced failure

Mouthfeel is as important as taste in the success of a plate or a food product. One important aspect of this complex multidimensional sensation is the mechanical behaviour at large deformation. Here we study the fracture behaviour of yoghurt, drawing a surprising parallel with brittle "hard" solids like composites or asphalt. Our results have implications for food design, and more broadly to the mechanics of biogels.

Talk given at Internation Symposium on Food Rheology and Structure, Zurich
See http://dx.doi.org/10.1103/PhysRevLett.113.038303

Transcript

1. Acid-induced protein gels: from gelation to stress-induced failure Mathieu Leocmach Laboratoire de physique, Ecole Normale Supérieure de Lyon  June 
2. Texture as important as taste 
3. Mouth feel A very complex, multidimensional sensation Behaviour of the food at large deformation? How does food break into pieces? Ductile fracture Irreversible deformation rubber lead butter Brittle fracture concrete asphalt glass 
4. The simplest Yoghurt Acid-set protein gel Water ( ◦C) Sodium caseinate (milk protein) % stable solution Glucono-δ-lactone (GDL) % ⇒ slow homogeneous acidification     isoelectric point pH ≈ . pH                 gelation time (h) G ,G (Pa) Kaláb (), Roefs & van Vliet (), Lucey & Singh () 
5. Linear rheology: Power law (visco)elastic solid stress → σ = Gγ ← strain storage →G + ıG ← loss −      G ∼ G ∼ f. Frequency (Hz) Storage and loss moduli (Pa) 
6. The yoghurt creep experiment σ A Taylor- Couette cell where the yogurt is made in situ ultrasonic velocimetry optical imaging A rheometer imposes a constant stress σ and records the strain γ(t) 
7. The yoghurt creep experiment power-law creep nucleation explosive regime σ = Pa −     − − − − t (s) strain rate ˙ γ (s−) 
8. Different (constant) stresses: universality −       − − − − − −   time (s) Strain rate ˙ γ (s−)  Pa     Normalisation τf failure time ˙ γmin minimum strain rate ⇒ Physical origin? − −       t/τf ˙ γ/ ˙ γmin power-law creep  . . . .      t/τf fracture nucleation − −       (τf − t)/τf explosive regime 
9. Power-law creep and plasticity “Andrade” creep () Power-law creep known in ductile solids for over a century Classically explained by disinclination dynamics in crystals Recently explained by plastic events in glasses Miguel et al., PRL  Any plastic event in yoghurt? Ultrasound velocimetry ⇒ local velocity maps T. Gallot et al., Rev. Sci. Instrum. ,  () homogeneous strain field (no wall slip, no shear band) if present, plastic events are below our resolution (a few µm) 
10. Is power-law creep damaging the structure? Stop creep much before (γ < .) fracture nucleation (γ ≈ ) Let relax ⇒ No complete recovery Reset deformation and start again ⇒ superimposable          . . . σ ← Pa σ ←  γ ←  time (h) strain γ Undamaged structure ⇒ Plasticity cannot explain power law Viscous dissipation 
11. Power-law creep as linear response −       G ∼ G ∼ f. Frequency (Hz) G , G (Pa) σ ∝ γfα Fourier − − − − − − → σ ∝ γt−α Constant σ γ(t) ∝ σtα d dt − − → ˙ γ(t) ∝ σtα− − − − − −       ˙ γ(t) ˙ γmin ∼ t τf −. t/τf ˙ γ/ ˙ γmin Power-law creep is the linear regime of the material up to % strain! explained without plasticity 
12. Explaining the explosive regime Fracture length − − −   . . . . . H ∼ ln τf −t τf (τf − t)/τf /H γ ∝ ∝ ln τf − t τf ˙ γ ∝ τf − t τf − − − − − −       ˙ γ(t) ˙ γmin ∼ τf τf −t (τf − t)/τf ˙ γ/ ˙ γmin ⇒ Explosive regime dominated by fracture growth 
13. Failure time & master curve           τf ∼ σ−. No yield stress! σ (Pa) τf (s) Basquin law τf ∼ σ−β fatigue (oscillatory stress) heterogeneous solids  . . . .  .  .  .  .  τmin t/τf ˙ γ/ ˙ γmin Master curve ˙ γ(t) ˙ γmin = λ t τf −. linear response + µ  − t/τf fractures ⇒ no room for plasticity 
14. Fibre bundle models σ model elastic fibres local yield strain local coupling Jagla et al., PRE  ˙ γ ˙ γ But yield stress built in power-law creep no master curve − −     t/τf ˙ γ/ ˙ γmin − −     (τf − t)/τf ˙ γ/ ˙ γmin 
15. Fibre bundle models Kun et al. PRL  Halász et al., PRE  elastic fibres local yield strain local coupling + damage accumulation model But no power-law creep too slow divergence D fractures           σ (Pa) τf (s) 
16. Creep and yielding summary failure involves a single time scale τf ∼ σ−. Basquin law reversible, homogeneous creep → irreversible fracture growth a single expression captures all the global rheological response − −       t/τf ˙ γ/ ˙ γmin  . . . .      t/τf − −       (τf − t)/τf a model soft solid well captured by fibre-bundle models 
17. Can we generalise to biogels? (physical gels Ebond kB T) Cell mechanics Electrophoresis Cosmetics Bacterial culture Food Sources Wikimedia Commons www.madaboutscience.com www.keautystore.com 
18. Merciless yoghurt breakers Leocmach et al. PRL ,  (), ArXiv . Christophe Perge Thibaut Divoux Sebastien Manneville PhD student CNRS researcher Professor E.N.S. Lyon CRPP Bordeaux E.N.S. Lyon Special thanks to Alan Parker (Firmenich) for prompting this study and providing casein & GDL 
20. Creep rheology: Three regimes primary secondary tertiary −       . . . . . time (s) strain γ  Pa     Failure at γ ≈  for a well defined time τf 