Florence Rouyer, Sylvie Cohen-Addad, Reinhard Höhler Aqueous foams have complex rheological properties. They show elastic behavior when subjected to stresses below a yield stress and they flow as non-Newtonian fluids for stresses beyond this characteristic value. The yielding behavior may depend on the flow history of the sample and the flow geometry of the experiment, possibly involving strain localization effects. These phenomena as well as the difficulty to characterize fully the relevant structural and physicochemical properties of a foam may explain the discrepancy between experimentally obtained values of the yield stress that can be found in the literature. Influence of flow geometry Large oscillatory strains in a cylindrical Couette cellInclined Plane  y = (1-  )  g sin   h = (1-  )  g sin  h f hfhf  z hh 45° hfhf Gillette 81% (Coussot et al, 1996) z  y  xz  (1-  )  g sin  (z max -z)   y yy g hh x (Di Federico, 1999)  Inclined Plane  Oscillatory strain yy Gas volume fraction  (f =1Hz)  f 21mm 25mm 5 mm Localization r +  r r ss  r    s /  r – s/r  r   1/r 2 s(r)/s max 1/r 2 (mm -2 ) r (mm)  (r)   =.5   =.7   =.5   =.7  =.9 Strain localization is observed around  = 0.6  0.1, well beyond yielding. Non-monotonous strain variation is a precursor of shear-banding. Localization is not located near the moving wall. Similar to observations in emulsions (Mason et al., 96). Yield stress data do not depend on the geometry Inclined plane set-up is not well adapted to the study of dry foam. Effects of controlled stress or strain and frequency Comparison with the literature Plotting  y /G' 0 allows to avoid uncertainties due to T and R determination..With this scaling, our results agree with previous ones (St Jalmes, Durian 1999, Mason et al & 1996). Low frequency oscillatory measurements of  y  /G' 0 give values different from that of steady shear measurements. Possible effect of localization in steady shear ? G'/ G' 0 G'' / G' 0  y Frequency (Hz) Controlled stress strain  y    y / G' 0   Controlled stress or strain experiments give similar results.  y   y / G' 0 z max 0 Elasto-plastic model Gillette 92%, 0.3 Hz Yield Strain Normalized Shear Modulus s : curvilinear coordinate s max Shear- banding G' G'' G' 0 G'' 0 Stress amplitude (Pa) Gillette 92% Shear Modulus (Pa) Stress Strain Time (s) Small amplitudeLarge amplitude  y  /G' 0  experiments Simu- lations  To Conclude Yielding measurement do not depend on geometry and controlled parameter (stress or strain), in the quasi-static regime. Shear modulus behavior of non-dissipative and dry foam is well described by the elasto-plastic model, but this model does not capture all the anharmonicity of the response. In low frequency oscillatory experiments, where localization effects can be excluded, yield strain is equal to yield stress divided by elastic shear modulus measured at small amplitude. The yield strain seems to be well defined for foams and emulsions, and varies as (  c )/ . Strain observation of the free sample surface in a Couette cell Comparison with the elasto-plastic model * * Weaire & Hutzler, 1999 Influence of physico-chemical properties  y G 0  y    y time  (t)  (t)  y G'/ G 0 G'' / G  y =  y /G 0 Stress Residual The complex shear modulus is well described by the elasto-plastic model, all the more if the foam is dry and weakly dissipative SGR (Sollich 98) ___ Elasto-plastic f   gillette 30 min 1 Hz  gillette 30 min.3 Hz 0.92  gillette 60 min 1 Hz  foam1 1 Hz  foam1.3 Hz 0.97 r  y Foam 1: Solution :AOK, PEO, LOH Gas : N 2 + perfluorohexan produced in a porous tube Bubble Radius: R = 23 µm Surface tension :  = 27 mN/m Foam characteristics Foam 2: Solution :TTAB, glycerol, LOH Gas : N 2 + perfluorohexan produced by whipping Bubble Radius: R = 18 µm Surface tension : T= 37 mN/m Normalized Shear Modulus G'' / G' 0 & G'/ G' 0 Localization onset Gillette: Commercial shaving cream Bubble Radius: R = 10 µm Surface tension :  = 30 mN/m G'' / G' 0 & G'/ G' 0  y  y  y G'' / G' 0 & G'/ G' 0 residual  y Elasto-plastic residual overestimates experimental values. SGR model residual agrees with experimental values, but experimental values of G' and G'' are not well described by this model. emulsions Princen, Kiss (1986 &1989)  Mason et al. (1995 & 1996) *  Mason et al. (1995 & 1996) * * * oscillatory measurements foams St Jalmes, Durian (1999) *  Khan (1988)  Gillette *  Foam1 *  Gopal, Durian (1999)  Kraynik et al. (2000)  Durian (1995) This work was presented at the 5th European Conference in foam, emulsions and applications, Champs-sur-Marne, France, July Is the yield stress of aqueous foam a well defined quantity ?