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Foam is described as an ensemble of independent films. Initially, the films are randomly oriented. The deformation of the material is affine (no rearrangements). 10°. left Cauchy –Green tensor:. 15°. shear. Coarsening rate. ·. ·. 10.

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Foam is described as an ensemble of independent films.

  • Initially, the films are randomly oriented.
  • The deformation of the material is affine (no rearrangements).

10°

left Cauchy –Green tensor:

15°

shear

Coarsening rate

·

·

10

  • Normal stress sensitivity (with equalsurface  1dm²)

Commercial Bohlin rheometer (CVOR150):  0.1 Pa

Our optimised rheometer:  0.001 Pa

Significant deviations at low amplitudes (0 < 0.1) with the 10° cone (trapped stresses stronger than with 15°)

With

trapped stresses

D. Hautemayou

Without

trapped stresses

Cone angle

Good agreement with the generalisedPoynting law (0  0.1)

Coarsening releases part of the stresses trapped due to the strain history.

=> more isotropic structure

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:

Princen’s 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 wt >>1: 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 <d>
  • 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.