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Spatial cooperativity in soft glassy flows


Amorphous glassy materials of diverse nature—concentrated emulsions, granular materials, pastes, molecular glasses—display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications1,2,3. A general feature of such systems, well documented yet not really understood, is the strongly nonlinear nature of the flow rule relating stresses and strain rates4,5. Here we use a microfluidic velocimetry technique to characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughnesses. We find evidence for finite-size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast to the classical nonlinearities of the rheological behaviour of amorphous materials, we show that a rather simple non-local flow rule can account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of cooperativity within the flow at these scales, that is unobservable in the liquid state (lower emulsion concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers (for example, coatings), these non-locality and cooperativity effects have parallels in the behaviour of other glassy, jammed and granular systems, suggesting a possible fundamental universality.

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Figure 1: Local flow curves measured by magnetic resonance imaging and microfluidic velocimetry.
Figure 2: Velocity profiles in microchannels with different widths w and confining wall roughness, corrected for the slip velocity.
Figure 3: Flow cooperativity length ξ as a function of emulsion volume fraction φ.


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Discussions with J.-L. Barrat and B. Andreotti are acknowledged. This project was supported by Rhodia, Région Aquitaine and the ANR. L.B. acknowledges support from the von Humboldt Foundation.

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Correspondence to A. Colin or L. Bocquet.

Supplementary information

Supplementary information

The Methods describe : (PDF 2789 kb)

1. the properties of the emulsions used in this study 2. their bulk rheological properties 3. microchannels fabrication and characteristics 4. velocimetry techniques (IRM and -PIV) 5. local density measurements

The Supplementary Figures and Legends present :

1. a light-scattering characterization of the polydispersities of the two sets of emulsions used in this study 2. pictures of the smooth and rough surfaces of the microchannels 3. a velocity profile of an emulsion below the jamming point, demonstrating a very good agreement with a shear-thinning model without non-locality effects. 4. further measurements of the local flow curves for various confinements and surface roughness, hereby complementing the results presented in the main text. 5. further measurements of velocity profiles in the jammed state, here for the emulsion with 36% polydispersity, at a volume fraction of 75%. As in the main text - for the 20% polydispersity emulsion-, the non-local model is able to reproduce all experimental results using a single cooperativity length. 6. same as Supplementary Figure 5, but for the emulsion with volume fraction 80%. 7. Surface rheology for the emulsion. 8. Comparison of the experimental velocity profiles measured in 125 and 250 microns wide channels, with predictions using the local Herschel-Bukley flow curve. 9. Comparison of experimental velocity profiles with predictions obtained from alternative models involving non-locality (as proposed in Ref. [27]) 10. Spatial dependence of the volume fraction for various pressure gradients and confocal image of the emulsion under flow. 11. Local flow curves for various confinement ratio, /w.

The Supplementary Tables gather :

1. the parameters for the Hershel-Buckley model describing the bulk flow curve of the various emulsions used in this study. 2. the main characteristics of the microchannels (length, width, height and roughness type)

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Goyon, J., Colin, A., Ovarlez, G. et al. Spatial cooperativity in soft glassy flows. Nature 454, 84–87 (2008).

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