Rheology of concentrated suspensions

Objectives

We have conducted fundamental studies on model suspension flows, namely non-Brownian spheres, deformable or not, with or without interactions, notably during the PhD theses of W. Chèvremont and M. Maleki.
 

Results

Viscous resuspension of rigid particles

In collaboration with G. Ovarlez (Bordeaux) and S. Manneville (Lyon), we revisited viscous resuspension experiments in a Couette geometry using X‑ray imaging. When particles are more or less dense than the suspending fluid, they can be resuspended by viscous forces. The advantage of X‑ray imaging in these opaque media is that it allows obtaining the concentration profile and thus determining the normal stresses along the vorticity direction. These experimental results made it possible to discriminate between various contradictory correlations reported in the literature.
It is now also possible to quantitatively describe the rheological properties of suspensions numerically. Many approaches exist, but either they rely on poorly physical assumptions that are difficult to validate, or they solve the governing equations rigorously but are then too costly to simulate a sufficient number of particles. In collaboration with B. Chareyre (3SR), we used a now-classical DEM approach, developing a physically realistic lubricated contact model, and were able to determine the full set of constitutive laws for non-Brownian rigid particle suspensions at low Re, in a quantitative and exhaustive manner. These results confirm the role of friction in particle suspensions, but above all provide robust empirical laws that can be used in continuum models.
 

Suspensions of soft particles

The PhD thesis of M. Maleki focused on deformable particle suspensions, which are much less documented than rigid particle suspensions. Beyond the additional degrees of freedom associated with particle deformability, the contact itself is expected to be very different. We successfully reproduced the viscous resuspension experiments described above, but for drop suspensions (i.e., emulsions). The experimental challenge lies in avoiding coalescence phenomena at high shear rates. As in the case of rigid particles, we measured the concentration profiles (this time by absorbance) and thus determined the normal stresses responsible for resuspension.
We found laws very similar to those governing rigid, frictional particles, but with a notable difference: the maximum volume fraction (i.e., where stresses diverge) is much higher than in the case of rigid spheres. Consequently, the normal stresses are significantly lower. Within the range of capillary numbers studied, it is not so much the deformability of the drops but rather the nature of the contact (which remains lubricated in this case) that accounts for this strong difference.

Capsules composed of an elastic shell and a liquid core constitute an intermediate system between drops and rigid spheres. Furthermore, they are of interest both as a model for biological systems and for their ability to encapsulate active ingredients. Although extensively studied in isolation, capsule suspensions have so far been primarily investigated numerically.
The challenge we overcame during M. Maleki’s thesis was associated with producing them in sufficient quantities and with controlled properties to obtain concentrated suspensions. The capsules are produced via membrane emulsification followed by an interfacial complexation step, and are characterized at high throughput using a microfluidic device. This approach allowed us to characterize the rheology of the produced suspensions.
Very unexpectedly, these suspensions behave like an attractive gel, exhibiting a yield stress even at low volume fractions. This is a highly original behavior, since unlike attractive gels composed of colloidal particles, the studied capsules are very large (over 100 microns) and non-Brownian. This has two interesting consequences: first, they exhibit a microstructure that depends on shear history (for example, similar to rigid particle suspensions, they show a minimum in viscosity after flow reversal); second, they flow in a manner very similar to a standard suspension, i.e., with a viscosity independent of shear rate.
Thus, they represent one of the rare examples of a Bingham fluid. The origin of this attractive interaction between capsules is likely Coulombic and is now the subject of a dedicated study.

References

Saint-Michel, B., Manneville, S., Meeker, S., Ovarlez, G., & Bodiguel, H. (2019). X-ray radiography of viscous resuspension. Physics of Fluids, 31(10).

Chèvremont, W., Bodiguel, H., & Chareyre, B. (2020). Lubricated contact model for numerical simulations of suspensions. Powder technology, 372, 600-610.

Chèvremont, W., Chareyre, B., & Bodiguel, H. (2019). Quantitative study of the rheology of frictional suspensions: Influence of friction coefficient in a large range of viscous numbers. Physical Review Fluids, 4(6), 064302.

Maleki, M., de Loubens, C., & Bodiguel, H. (2022). Viscous resuspension of droplets. Physical Review Fluids, 7(1), L011602.

Maleki, M., de Loubens, C., Xie, K., Talansier, E., Bodiguel, H., & Leonetti, M. (2021). Membrane emulsification for the production of suspensions of uniform microcapsules with tunable mechanical properties. Chemical Engineering Science, 237, 116567.

Maleki, M., Bodiguel, H., & de Loubens, C. (2025). Suspensions of attractive microcapsules: A noncolloidal fragile gel?. Journal of Rheology, 69(2), 121-130.