Experiment: Creep rheometry + in situ DWS light scattering

1. Sylvie Cohen-Addad, Reinhard Höhler, Yacine Khidas Jo ho F1 F3 F2 Only two relaxation processes ! Interplay between interfacial rheology, bubble rearrangements and the slow macroscopic rheological response of aqueous foams 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 Possible origins of the low frequency dissipation Introduction • 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 Gillette foam Age  100 min Cohen-Addad, Hoballah, Höhler PRE 1998 Data from Gopal, Durian PRL 2003 • 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 Linear elasticity described by Princen law* Surface tension T1 rearrangement : Can coarsening induced rearrangements explain the low frequency dissipation ? Static shear modulus * Princen, Kiss 1986; Mason, Bibette, Weitz 1995; Saint-Jalmes, Durian 1999 Mean bubble diameter A simple mesoscopic steady creep model Experiment: Creep rheometry + in situ DWS light scattering Response to a step stress : Samples : s 0 • Hypotheses • The sample is subjected to constant shear stresss 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 Rper units of volume and time. • 92% gas volume fraction • Different coarsening rates Yield stress time t Fast Intermediate Applied stress s Slow time Shear compliance J(t) = g/s DJ Origin of the long time relaxation Origin of the short time relaxation: Scaling with bubble size Dt Jeo h1 time J1 J1 Jeo = Jo + J1 Increase of compliance expected due to temporary local loss of rigidity: DJ/Jeo R V Dt Predicted creep rate : R can be measured by Diffusing Wave Spectroscopy R = 1/(toVo) V should be of the order: a few (bubble diameters)3 Volume fraction rearranged during a small time interval Dt J1  d same scaling as Princen law. h1d-1as predicted by Buzza et al. if dilatational surface viscosity dominates the dissipation. Characteristic time scale t1 = J1h1 independent of d ! • Measured volume of a rearranged zone : V  (3 d)3 • Agreement with the model Conclusions and outlook 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 !): L Forces acting on a Plateau border : Edwards, Brenner, Wasan (1991) Creep deformation • 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. Surface tension Dilatational surface viscosity 0 Time Calculated relaxation time : t1k / T • 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. • Ultimate goal : Understanding the link between local physico-chemical processes and macroscopic foam rheology. Gillette: t15 s k 0.15kg s-1 AOK foams (sodium a- olefine sulfonate + PEO + Dodecanol): t13 s k 0.05kg s-1Consistent with values reported for similar mixed surfactant systems Djabbarah, Wasan 1982 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