Experiment: Creep rheometry + in situ DWS light scattering Sylvie Cohen-Addad, Reinhard Höhler, Yacine Khidas We have studied the slow linear viscoelastic.

Presentation on theme: "Experiment: Creep rheometry + in situ DWS light scattering Sylvie Cohen-Addad, Reinhard Höhler, Yacine Khidas We have studied the slow linear viscoelastic."— Presentation transcript:

1 Experiment: Creep rheometry + in situ DWS light scattering Sylvie Cohen-Addad, Reinhard Höhler, Yacine Khidas We have studied the slow linear viscoelastic response of wet aqueous foams by macroscopic creep compliance measurements, combined to a diffusing-wave spectroscopy investigation of the local dynamics. The data strongly suggest that this rheological response arises from two distinct relaxation mechanisms: The first is due to the coarsening induced bubble rearrangements and governs the steady state creep, the second results from the interplay between surface tension and surface viscosity of the gas-liquid interfaces and gives rise to a transient relaxation. Slow linear viscoelastic relaxations in coarsening foams Introduction Cohen-Addad, Hoballah, Höhler PRE 1998 Gillette foam Age  100 min Data from Gopal, Durian PRL 2003 Static shear modulus * Princen, Kiss 1986; Mason, Bibette, Weitz 1995; Saint-Jalmes, Durian 1999 Linear elasticity described by Princen law* Mean bubble diameter Surface tension Possible origins of the low frequency dissipation At the mesoscopic scale: Dissipation may be due to elastic energy irreversibly lost upon local structural rearrangements. Sollich et al PRL 1997; Hébraud et al PRL 1998 Coarsening unjams foams. Gopal, Durian 2003 At the film scale: Fluid transport in films and Plateau borders Intrinsic surface viscosity of the gas-liquid interfaces Resistance to diffusion from the surfactant Buzza, Lu, Cates 1995; Edwards, Wasan 1996 Can coarsening induced rearrangements explain the low frequency dissipation ? A simple mesoscopic steady creep model Hypotheses  The sample is subjected to constant shear stress  far below the yield stress.  The stress is relaxed locally upon randomly dispersed coarsening induced rearrangements.  Rearrangements have a characteristic volume V and occur at a rate R per units of volume and time. Volume fraction rearranged during a small time interval  t Increase of compliance expected due to temporary local loss of rigidity:  J/J eo  R V  t Predicted creep rate : R can be measured by Diffusing Wave Spectroscopy R = 1/(  o V o ) V should be of the order: a few (bubble diameters) 3 Applied stress  time Shear compliance J( t ) =  J eo JJ tt Samples : 92% gas volume fraction Different coarsening rates Fast Slow Intermediate Response to a step stress :  0 Yield stress Only two relaxation processes ! Origin of the long time relaxation Measured volume of a rearranged zone : V  (3 d) 3 Agreement with the model oo JoJo J1J1 J eo = J o + J 1 J1J1 11 J 1  d same scaling as Princen law.  1  d -1 as predicted by Buzza et al. if dilatational surface viscosity dominates the dissipation. Characteristic time scale  1 = J 1  1 independent of d ! Origin of the short time relaxation: Scaling with bubble size Gillette:  1  5 s    0.15 kg s -1 AOK foams ( sodium  olefine sulfonate + PEO + Dodecanol):  1  3 s    0.05 kg s -1 Consistent with values reported for similar mixed surfactant systems Djabbarah, Wasan 1982 Forces acting on a Plateau border : Edwards, Brenner, Wasan (1991) Surface tension Dilatational surface viscosity F1F1 F2F2 F3F3 L Calculated relaxation time :     /  2D model of transient structural relaxation  The viscoelastic dissipation in the linear regime, at low frequency, may indeed be explained by two well defined processes (no glassy dynamics !): Creep deformation Time 0  The contribution of the rearrangements to the slow rheological response is well modelised by a mesoscopic approach based on coarsening dynamics. A full understanding will require to consider film interfacial properties. In the limit of long times, dissipation arises from elastic energy lost upon coarsening induced bubble rearrangements. At times of the order of a few seconds, dissipation arises from a structural relaxation which is governed by the interfacial rheology.  Ultimate goal : Understanding the link between local physico-chemical processes and macroscopic foam rheology. Conclusions and outlook T1 rearrangement : time t This work was presented at the 5th European Conference in foam, emulsions and applications, Champs-sur-Marne, France, July 2004. Relevant publication : Cohen-Addad, Höhler, Khidas, Phys. Rev. Lett. 92, 2004 Interplay between interfacial rheology, bubble rearrangements and the slow macroscopic rheological response of aqueous foams Interplay between interfacial rheology, bubble rearrangements and the slow macroscopic rheological response of aqueous foams