1. Vincent Labiausse, Reinhard Höhler, Sylvie Cohen-Addad Visco-elastic behaviour of aqueous foams * Princen, Kiss 1986; Mason, Bibette, Weitz 1995; Saint-Jalmes, Durian 1999 Princen’s law *: 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 ? Complex shear modulus: solid liquid plastic N 1 =  11 -  22 N 2 =  22 -  33 Elastic normal stresses differences N 1 and N 2  Stationary flow Weissenberg effect:  Definition  Elastic regime Poynting effect: Valid for any elastic isotropic material  Foam is described as an ensemble of independent films.  Initially, the films are randomly oriented.  The deformation of the material is affine (no rearrangements). left Cauchy –Green tensor: shear Höhler, Cohen-Addad, Labiausse, J.Rheol. 2004 * Doi and Ohta 1991 Measuring N 1 in aqueous foams is difficult because of uncontrolled trapped stresses superpose to applied stress : there are no data in the literature. A constitutive law of Mooney-Rivlin type, rigorously developed starting from the physical ideas of the model of Doi and Otha: Do foams, which are visco-elastic and plastic, obey the Poynting law ? Examples: Without trapped stresses With trapped stresses Effect of trapped stresses: The first normal stress difference induced by oscillatory shear Effect of randomly oriented trapped stresses on P: For elastic material, Poynting law: P = 1 Visco-elastic generalisation for a nonlinear Maxwell liquid, if    >>1: P = 1 Development of a new rheometer optimised for measuring N 1  Cone and plate geometry: Stress heterogeneity for  = 15°,   7%  Normal stress sensitivity ( with equal surface  1dm²) Commercial Bohlin rheometer (CVOR150):  0.1 Pa Our optimised rheometer:  0.001 Pa R = 6 cm D. Hautemayou Sample characteristics No coalescence Negligible drainage Stability: Mean bubble diameter Coarsening rate Controlled variation of the parameters: Foam types (µm) (µm/min) AOK- N 2 - C 6 F 14 Gas: nitrogen + perfluorohexan 470.4 AOK- N 2 Gas: nitrogen 1564.6 · Dry foams  = 97% Foaming solution: Sodium  -olefine Sulfonate + PEO + Dodecanol · Results and discussion Good agreement with the generalised Poynting law (  0  0.1)  = 97% 10° 15° Cone angle Significant deviations at low amplitudes (  0 < 0.1) with the 10° cone (trapped stresses stronger than with 15°) AOK-N 2 Coarsening rate 10 Coarsening releases part of the stresses trapped due to the strain history. => more isotropic structure AOK-N 2 -C 6 F 14 Conclusions We propose a non-linear viscoelastic constitutive model predicting the first normal stress difference N 1, based on a physical description of foams. We have carried out the first experimental study of N 1 for aqueous foams. When the effects of trapped stresses are minimised, our results agree with the model. Introduction This work was presented at the 5th European Conference in foam, emulsions and applications, Champs-sur-Marne, France, July 2004. Shear-induced normal stress differences in aqueous foams