Vincent Labiausse, Reinhard Höhler, Sylvie Cohen-Addad

1. 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.