Wide-gap Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging

G. Ovarlez, S. Rodts, A. Ragouilliaux, P. Coussot, J. Goyon, and A. Colin

Phys. Rev. E 78, 036307 – Published 10 September 2008

Abstract

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions, with droplet size ranging from $0.3 to 40 μ m$ , in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear in wide-gap Couette flows, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon et al. [Nature (London) 454, 84 (2008)]: the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of Bécu et al. [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion.

Received 20 May 2008

DOI:https://doi.org/10.1103/PhysRevE.78.036307

Authors & Affiliations

G. Ovarlez¹, S. Rodts¹, A. Ragouilliaux¹, P. Coussot¹, J. Goyon², and A. Colin²

¹Université Paris Est-Institut Navier, LMSGC (LCPC-ENPC-CNRS) 2, allée Kepler, 77420 Champs-sur-Marne, France
²LOF, Université Bordeaux 1, UMR CNRS-Rhodia-Bordeaux 1 5258, 33608 Pessac cedex, France

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Vol. 78, Iss. 3 — September 2008

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Images

Figure 1
Concentration profiles observed within the gap of a Couette geometry after shearing a $0.3 − μ m$ adhesive emulsion for 10 000 revolutions (squares), and a $40 − μ m$ nonadhesive emulsion for 20 000 revolutions (open circles).Reuse & Permissions
Figure 2
(Color online) (a) Dimensionless velocity profiles for the steady flows of a $0.3 − μ m$ adhesive emulsion, at various rotational velocities ranging from $5 to 100 rpm$ ; the line is the theoretical dimensionless velocity profile for a Newtonian fluid. (b) The same plot for a $1 − μ m$ nonadhesive emulsion. (c) The same plot for a $6.5 − μ m$ adhesive emulsion. (d) The same plot for a $6.5 − μ m$ nonadhesive emulsion. (e) The same plot for a $40 − μ m$ nonadhesive emulsion.Reuse & Permissions
Figure 3
The same plots as in Fig. 2 in log scale (for readability, not all profiles are plotted). The solid lines of Fig. 3a are the velocity profiles predicted by a Herschel-Bulkley law.Reuse & Permissions
Figure 4
(a) Macroscopic measurements: stationary torque vs rotational velocity for the steady flows of a $0.3 − μ m$ adhesive emulsion; inset: torque vs angular displacement for various rotational velocities ranging between 0.01 and $50 rpm$ (bottom to top). (b) Constitutive law inferred from the purely macroscopic measurements thanks to Eqs. (5, 8); the solid line is a Herschel-Bulkley fit $τ = τ_{c} + η_{H B} {\dot{γ}}^{n}$ of the data with $τ_{c} = 77 Pa$ , $η_{H B} = 15.4 Pa s$ , and $n = 0.5$ .Reuse & Permissions
Figure 5
(Color online) (a) Constitutive law measured locally in the gap of a Couette cell for the flows of (from top to bottom) a nonadhesive $1 − μ m$ emulsion, a nonadhesive $6.5 − μ m$ emulsion, and an adhesive $6.5 − μ m$ emulsion; the solid line is a Herschel-Bulkley fit $τ = τ_{c} + η_{H B} {\dot{γ}}^{n}$ of the data with $n = 0.5$ for all materials, $τ_{c} = 59 Pa$ and $η_{H B} = 11.5 Pa s$ for the nonadhesive $1 − μ m$ emulsion, $τ_{c} = 12 Pa$ and $η_{H B} = 11.5 Pa s$ for the nonadhesive $6.5 − μ m$ emulsion, and $τ_{c} = 21.5 Pa$ and $η_{H B} = 15 Pa s$ for the adhesive $6.5 − μ m$ emulsion. (b) Constitutive law measured locally in the gap of a Couette cell for the flows of a $0.3 − μ m$ adhesive emulsion (empty symbols); the solid line is a Herschel-Bulkley fit $τ = τ_{c} + η_{H B} {\dot{γ}}^{n}$ of the data with $τ_{c} = 77 Pa$ , $η_{H B} = 15.4 Pa s$ , and $n = 0.5$ . The crosses are the data extracted from the analysis of the purely macroscopic measurements [see Fig. 4b].Reuse & Permissions
Figure 6
(a) Dimensionless velocity profiles for the steady flows of a $6.5 − μ m$ adhesive emulsion, for a 10- and a $20 − rpm$ rotational velocity. (b) Dimensionless velocity profiles expected near the walls at 10 and $20 rpm$ ; the velocities are computed thanks to the local shear rate measurements performed at $50 rpm$ .Reuse & Permissions

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