Shearinduced normal stress differences in aqueous foams

1
Shear-induced normal stress differences in
aqueous foams
Vincent Labiausse, Reinhard Höhler, Sylvie
Cohen-Addad
Visco-elastic behaviour of aqueous foams
Elastic normal stresses differences N1 and N2
Introduction

• Definition

N1 ?11 - ?22 N2 ?22 - ?33
solid
liquid
plastic
Complex shear modulus
Since foams can undergo large elastic strains,
their behaviour must present significant
non-linear effects, like for instance rubber. How
can we study these effects which have been
predicted but never measured ?

• Stationary flow
• Weissenberg effect

Princens law

• Elastic regime
• Poynting effect

Valid for any elastic isotropic material
Princen, Kiss 1986 Mason, Bibette, Weitz 1995
Saint-Jalmes, Durian 1999
Do foams, which are visco-elastic and plastic,
obey the Poynting law ?
The first normal stress difference induced by
oscillatory shear

• Measuring N1 in aqueous foams is difficult
  because of uncontrolled trapped stresses
  superpose to applied stress there are no data
  in the literature.

• Effect of trapped stresses

• A constitutive law of Mooney-Rivlin type,
  rigorously developed starting from the physical
  ideas of the model of Doi and Otha

Effect of randomly oriented trapped stresses on
P

Examples
For elastic material, Poynting law P 1
Visco-elastic generalisation for a nonlinear
Maxwell liquid, if w t gtgt1 P 1
Doi and Ohta 1991
Höhler, Cohen-Addad, Labiausse, J.Rheol. 2004
Sample characteristics
Results and discussion
Foaming solution Sodium a-olefine Sulfonate
PEO Dodecanol
? 97
AOK-N2
AOK-N2-C6F14
Stability

• No coalescence
• Negligible drainage

Controlled variation of the parameters

• Mean bubble diameter ltdgt
• Coarsening rate

Dry foams f 97
Development of a new rheometer optimised for
measuring N1

• Cone and plate geometry

Conclusions

• We propose a non-linear viscoelastic
  constitutive model predicting the first normal
  stress difference N1, based on a physical
  description of foams.
• We have carried out the first experimental study
  of N1 for aqueous foams.
• When the effects of trapped stresses are
  minimised, our results agree with the model.

Stress heterogeneity for ? 15, ?? ? 7
R 6 cm
This work was presented at the 5th European
Conference in foam, emulsions and applications,
Champs-sur-Marne, France, July 2004.