%0 Book Section %1 statphys23_0626 %A Marmottant, P. %A Dollet, B. %A Raufaste, C. %A Graner, F. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K foams rheology statphys23 topic-7 %T Understanding the macroscopic flow of a complex fluid from its individual constituents: the example of a transparent foam %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=626 %X INTRODUCTION Foams prove to be convenient materials for the study of complex fluids. At large scales compared to the bubble size, they behave as a continuous medium. This medium is an elastic solid at low stress, undergoes plastic deformation at larger stress, and flows as a liquid for sufficient stress. Its individual constituents, bubbles, are easily followed by image analysis of a 2D flow. Each bubble acts as a tracer: not only for the velocity, but also for the local elastic and plastic deformation. In this talk, we will be concerned by the statistical tools necessary to link the microscopic motion of the bubbles to the continuous macroscopic deformations of the material. The macroscopic behaviour of the flow then needs to be described by a constitutive equation relating stresses to strains, that would unite elastic, plastic and viscous properties. FROM INDIVIDUAL MOTIONS TO MACROSCOPIC FLOW: STATISTICAL TOOLS We study an experiment where a foam is forced to flow in 2D around an obstacle (see figure). The image analysis provides the centers of the bubbles, from which we construct a network of links between neighbour centers. We introduce statistical tools to measure three coarse-grained tensorial quantities: (i) the local elastic deformation of the foam is obtained from the deformation of the network, averaged in a mesoscopic box. (ii) the plastic deformations result from localized bubble rearrangements. The rearrangements are monitored on the evolution of the links: a link disappear while a new link appears. We describe their orientation and the frequency of events using a topological tensor (see figure). The topological tensor makes the link with the macroscopic plasticity tensor. Indeed foams, and emulsions, have the particularity that plastic irreversibility is strictly due to rearrangements. It is for instance not the case with granular material where irreversibility does not necessary implies rearrangements. (iii) the fluid flow is measured by averaging the tracer velocities. CONSTITUTIVE EQUATION OF THE FOAM FLOW Having all the map of tensorial deformations accessible, we can test a constitutive equation for the dynamics of the flow (rheology), LOCALLY, throughout the whole domain of foam flow. A simple elasto-plastic model predicts correctly the local rheology of the flow: plasticity (originating from rearrangements) is aligned with elastic stresses, and its rate is proportional to the total strain rate. CONCLUSION We presented statistical coarse-graining tools that allow to describe the foam as a continuous medium with fluid, elastic and plastic properties, and that allowed us to test the rheological properties. The statistical tools we introduced can be applied to all divided matter systems that undergo neighbour rearrangements: emulsions, granular materials, colloids, polycristals, biological tissues of cells.

@incollection{statphys23_0626, abstract = {INTRODUCTION Foams prove to be convenient materials for the study of complex fluids. At large scales compared to the bubble size, they behave as a continuous medium. This medium is an elastic solid at low stress, undergoes plastic deformation at larger stress, and flows as a liquid for sufficient stress. Its individual constituents, bubbles, are easily followed by image analysis of a 2D flow. Each bubble acts as a tracer: not only for the velocity, but also for the local elastic and plastic deformation. In this talk, we will be concerned by the statistical tools necessary to link the microscopic motion of the bubbles to the continuous macroscopic deformations of the material. The macroscopic behaviour of the flow then needs to be described by a constitutive equation relating stresses to strains, that would unite elastic, plastic and viscous properties. FROM INDIVIDUAL MOTIONS TO MACROSCOPIC FLOW: STATISTICAL TOOLS We study an experiment where a foam is forced to flow in 2D around an obstacle (see figure). The image analysis provides the centers of the bubbles, from which we construct a network of links between neighbour centers. We introduce statistical tools to measure three coarse-grained tensorial quantities: (i) the local elastic deformation of the foam is obtained from the deformation of the network, averaged in a mesoscopic box. (ii) the plastic deformations result from localized bubble rearrangements. The rearrangements are monitored on the evolution of the links: a link disappear while a new link appears. We describe their orientation and the frequency of events using a topological tensor (see figure). The topological tensor makes the link with the macroscopic plasticity tensor. Indeed foams, and emulsions, have the particularity that plastic irreversibility is strictly due to rearrangements. It is for instance not the case with granular material where irreversibility does not necessary implies rearrangements. (iii) the fluid flow is measured by averaging the tracer velocities. CONSTITUTIVE EQUATION OF THE FOAM FLOW Having all the map of tensorial deformations accessible, we can test a constitutive equation for the dynamics of the flow (rheology), LOCALLY, throughout the whole domain of foam flow. A simple elasto-plastic model predicts correctly the local rheology of the flow: plasticity (originating from rearrangements) is aligned with elastic stresses, and its rate is proportional to the total strain rate. CONCLUSION We presented statistical coarse-graining tools that allow to describe the foam as a continuous medium with fluid, elastic and plastic properties, and that allowed us to test the rheological properties. The statistical tools we introduced can be applied to all divided matter systems that undergo neighbour rearrangements: emulsions, granular materials, colloids, polycristals, biological tissues of cells.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Marmottant, P. and Dollet, B. and Raufaste, C. and Graner, F.}, biburl = {https://www.bibsonomy.org/bibtex/2359db12dc3ebb01f46c4cb240dc2e54b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {3a7282f5b77da1389bd57a9a47451c9b}, intrahash = {359db12dc3ebb01f46c4cb240dc2e54b}, keywords = {foams rheology statphys23 topic-7}, month = {9-13 July}, timestamp = {2007-06-20T10:16:25.000+0200}, title = {Understanding the macroscopic flow of a complex fluid from its individual constituents: the example of a transparent foam}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=626}, year = 2007 }