Mechanics of yield stress fluids

Objectives

We pursue fundamental research in fluid mechanics using two complementary approaches: on one hand, experiments performed on model non-thixotropic yield-stress fluids using original experimental setups, and on the other hand, the development of viscoplastic and elasto-viscoplastic numerical models. The elasto-viscoplastic modeling is based on a finite element method with Lagrangian integration points (MEFPIL), implemented in collaboration with the 3SR laboratory. The main objective is to precisely determine the role of the solid–liquid transition, taking into account both bulk phenomena and those occurring at fluid–solid interfaces.
Two aspects have been investigated in depth, revealing original results on these fundamental configurations, thereby providing a better understanding of fluid–structure interactions in various contexts, with implications for engineering and modeling of non-Newtonian flows. Finally, from a more applied perspective, yield-stress fluids have been formulated in highly alkaline media for redox flow batteries.

Results

Flow around obstacles

In the field of non-inertial flows, the focus has been on determining the hydrodynamic drag and lift forces acting on a cylinder or a plate with variable inclination, either in interaction with or isolated from a solid surface. Numerical simulations using a regularized viscoplastic model were able to reproduce the experimental results. Both experimentally and numerically, a significant influence of the initial stress state of the elasto-viscoplastic material is observed in the regime where yield effects dominate over viscous effects. The results obtained with the MEFPIL method are of the same order of magnitude as those from experiments.
In the domain of strongly inertial flows, the experimental influences of yield stress and rheofluidization on the onset of vortex shedding, the characteristics of wakes behind a cylinder, and the vortex shedding frequency in unsteady regimes have been quantified. The presence or absence of wall slip at the cylinder significantly alters the flow. Purely viscoplastic modeling is able to correctly simulate these flows.

Rayleigh–Bénard convection in yield-stress fluids

Thermal convection within an elasto-viscoplastic gel (Carbopol gel) subjected to Rayleigh–Bénard convection was studied experimentally. The transition from the conductive regime to the convective regime was determined according to the Schmidt–Milverton principle. The critical values of the ratios (yield stress to buoyancy effects) and (yield stress to elastic modulus), characterizing the onset of convective instabilities, were quantified. An increase in yield stress delays the onset of convection, while elasticity promotes it.
Furthermore, the critical value for the onset of convective instability is strongly influenced by the presence or absence of wall slip in the yield-stress fluid, with slip favoring the onset. Elasto-viscoplastic numerical modeling using the MEFPIL method of the convection onset criteria provides values of the same order of magnitude as the experimental results, both under slip and adhesion conditions. It also provides access to the kinematic and stress fields.
Finally, detailed experimental study of fluid motion below the critical convection onset, i.e., in the conductive regime, revealed an original oscillatory motion within the gel. Tracer particles describe oscillating loops around their initial positions. As the critical value for convection onset is approached, the loops persist, but particles progressively shift relative to their initial positions. These oscillations take the form of periodic progressive waves, with elastic effects playing a decisive role in their appearance. This study benefited from collaboration with C. Métivier from LEMTA, Nancy.

Formulation and rheology of electrolytes for Zn–air redox flow batteries

In order to develop efficient and flexible stationary energy storage systems, we focused on the deployment of zinc–air redox flow batteries (Zn–air RFBs), specifically on the formulation of a liquid anode electrolyte in which zinc microparticles are suspended.
A first challenge was addressed by formulating a polymer gel electrolyte (GPE) in a highly alkaline medium (pH 14) from a potassium hydroxide solution and a combination of two gelling agents, polyacrylic acid (PAA, Carbopol®) and a clay. The elasto-visco-plastic character, related to the presence of PAA in the formulation, as well as its stability, were demonstrated through systematic rheometry tests, using a specific geometry developed, calibrated, and validated for this study.
These GPEs are then used as a matrix to suspend zinc particles (density 7) and prevent their sedimentation, another challenge addressed in this work. Using inverse rheometry and UV–Vis spectroscopy, we highlighted and analyzed the zinc–PAA interactions. We showed that parameters such as ionic strength, adsorption of the PAA microgel on zinc surfaces, and zinc complexation mechanisms that can occur in alkaline conditions affect the rheological behavior of the matrix, allowing adjustment of the yield stress and control of suspension stability.
Finally, we demonstrated that the resulting gelled network allows the ionic mobility necessary for electrochemical activity. The combined effects of yield stress and conductivity on battery performance were quantified.

References

Mossaz, S. et al., Two-dimensional unsteady inertial flows of a yield stress fluid around a cylinder, Journal of Non-Newtonian Fluid Mechanics, 2021

Jossic, L., et al., Drag on a plate perpendicular to the flow of an elasto-viscoplastic fluid, Discov Mechanical Engineering, 2023

Ouattara, Z. et al., Influence of the inclination of a plate on forces generated in flows of Newtonian and yield stress fluids, Chem. Eng. Sci., 2019 

Ouattara, Z et al., Flow of a Newtonian fluid and a yield stress fluid around a plate inclined at 45° in interaction with a wall, AIChE, 2019

Metivier, C. et al., Oscillatory Rayleigh–Bénard Convection in elasto-viscoplastic gels, J. Non-Newtonian Fluid Mech., 2020

Choi et al, Use of Carbon Additives towards Rechargeable Zinc Slurry Air Flow Batteries, Energies, 2020

Milian et al, Rheological behavior of gel polymer electrolytes: yield stress and viscoelasticity, Rheol. Acta, 2022

Milian et al, Formulation and characterization of zinc slurries for zinc slurry – Air redox flow battery: A rheological approach,  J. Power Sources 2023

Milian et al, Investigating the interactions between Carbopol® and zinc particles within the context of a zinc-air redox flow batteries application, Rheol. Acta, 2024