Yielding and Flow of Soft-Jammed Systems in Elongation

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Yielding and Flow of Soft-Jammed Systems in Elongation

X. Zhang, O. Fadoul, E. Lorenceau, and P. Coussot

Phys. Rev. Lett. 120, 048001 – Published 23 January 2018

Abstract

So far, yielding and flow properties of soft-jammed systems have only been studied from simple shear and then extrapolated to other flow situations. In particular, simple flows such as elongations have barely been investigated experimentally or only in a nonconstant, partial volume of material. We show that using smooth tool surfaces makes it possible to obtain a prolonged elongational flow over a large range of aspect ratios in the whole volume of material. The normal force measured for various soft-jammed systems with different microstructures shows that the ratio of the elongation yield stress to the shear yield stress is larger (by a factor of around 1.5) than expected from the standard theory which assumes that the stress tensor is a function of the second invariant of the strain rate tensor. This suggests that the constitutive tensor of the materials cannot be determined solely from macroscopic shear measurements.

Received 10 September 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.048001

Physics Subject Headings (PhySH)

Jamming Rheology Rheology techniques Strain Viscoplasticity Wall slip

Polymers & Soft MatterFluid DynamicsInterdisciplinary Physics

Authors & Affiliations

X. Zhang¹, O. Fadoul¹, E. Lorenceau², and P. Coussot¹

¹Université Paris-Est, Laboratoire Navier (ENPC-IFSTTAR-CNRS), 2 Allée Kepler, 77420 Champs sur Marne, France
²Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France

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Vol. 120, Iss. 4 — 26 January 2018

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Images

Figure 1
Force vs distance during a traction experiment for a direct emulsion (82%) with rough plates (thin red curves) or smooth surfaces (thick dark blue curves) for different initial aspect ratios (corresponding to first point of curves on the left) at $U = 0.01 mm / s$ ( $Ω = 3 ml$ ). The very thick light blue line corresponds to $U / h = const = 0.01 s^{- 1}$ . The dashed line is the lubrication model (see text), and the dotted line is the standard theoretical curve for slow elongation.
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Figure 2
Successive views for different plate distances during relative motion of two plates in contact via an emulsion (82%) (yellow region). Here, only one side (relative to the axis) is (partially) shown (the zones between the yellow regions and the vertical axis are, in fact, filled with material), the central axis is shown in blue on the right, and the mean sample radius is represented by horizontal arrows.
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Figure 3
Force vs height curve with smooth surfaces during traction on a yield stress fluid (emulsion 82%) for $Ω = 3 ml$ and different $U$ [(dotted lines) from bottom to top, 0.01, 0.02, 0.03, 0.05, 0.07, $0.1 mm s^{- 1}$ ] or $\dot{ϵ}$ [(continuous curves) from bottom to top, 0.01, 0.02, $0 .03 s^{- 1}$ ]. The straight dotted line is the standard expression for normal force in elongation. The lower inset shows the rescaled residual force (see text) as a function of the distance for the above data (red) at constant $U$ and for data obtained with emulsions at 76% (light blue) and 85% (dark blue) at $U = 0.01$ and $0 .05 mm s^{- 1}$ . The dashed line has a slope of $- 3$ in logarithmic scale. The higher inset shows the rescaled residual force for data of the main graph (red) at constant $\dot{ϵ}$ and for emulsions at 76% (light blue) and 85% (dark blue) at 0.01 and $0 .04 s^{- 1}$ , and 82% with a glycerol solution (black) at $\dot{ϵ} = 0.01$ and $0 .04 s^{- 1}$ . Data for an emulsion with smaller droplet size (i.e., $0.7 μ m$ ) at $\dot{ϵ} = 0.01$ and $0 .04 s^{- 1}$ are also shown (green). The dotted line has a slope $- 2$ in logarithmic scale. No particular tendency of variation as a function of $U$ or $\dot{ϵ}$ may be observed in the inset graphs.
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Figure 4
Rescaled force vs height during traction tests at a constant strain rate ( $0 .01 s^{- 1}$ ) for emulsions at a concentration of 82% for different volumes (1, 2, 3, and 4 ml) (continuous red curves); emulsions at concentrations 76% (dotted light blue) (3 ml), 85% (dotted dark blue) (1 and 3 ml), and 87% (brown dash dotted line) for 3 ml; a Carbopol gel (dashed green) for 1 and 3 ml. The dotted straight line corresponds to $σ = \sqrt{3} τ_{c}$ . Reproducibility tests show that the uncertainty on these data is 10% (see Ref. [10]). The inset shows the flow curves in simple shear for the three emulsions (from bottom to top) 76%, 82%, 85%, 87%. The dotted lines show the level of yield stress as deduced from creep tests. The uncertainty on these values is less than 5% (see Ref. [10]).
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