Flow-induced anisotropic mechanical response of dense suspensions

Project Information

SuspenseStory

Grant agreement ID: 101149195

DOI

10.3030/101149195

Project closed

EC signature date 28 March 2024

Start date 1 June 2024

End date 31 July 2026

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 211 754,88

Coordinated by

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France

Periodic Reporting for period 1 - SuspenseStory (Flow-induced anisotropic mechanical response of dense suspensions)

Reporting period: 2024-06-01 to 2026-07-31

Summary of the context and overall objectives of the project

Particles suspended in liquids, known as suspensions, are prevalent worldwide, from everyday products like creams and pastes to critical industries like pharmaceuticals and vaccines. Suspension rheology (that is, what is the suspension stress in a given flow condition) is key to many industrial processes, and is currently still an open problem. Suspensions may show many complex flow behaviors such as shear thickening (viscosity increasing with flow rate), thinning (viscosity decreasing with flow rate), and jamming (complete loss of flowability). Often, particles are large enough to not be affected by Brownian motion. External forces or driving are necessary for their motion, regardless of whether they are in a jammed or unjammed state. Therefore these concentrated suspensions exhibit mechanical properties characterized by significant dependence on previous deformation history. Suspensions of hard particles show dramatic viscosity reduction upon reversal of the flow direction (known as “shear reversal”), or under high-frequency orthogonal superposition, that is, when applying a secondary oscillating shear orthogonal to the main flow direction. This is due to the presence of a shear-induced anisotropic microstructure, which is particularly resistant to the kind of flow that gave rise to it, but not so much to flows in other directions.

Recent experiments and numerical simulations started to characterize the mechanical response of non-Brownian suspensions of hard particles to a change of flow direction. This project aims at fully characterizing the relation between flow history and mechanical response using numerical simulations and at using it to develop a constitutive model, that is, a set of equations able to predict the stress in arbitrary flow conditions. The main expected result is a quantitative constitutive model for non-Brownian suspensions, which is currently still lacking, despite decades of attempts and progress in this direction. The originality of our approach is to guide, test and validate our modelling with the rich data sets obtained from our simulations, which probe the tensorial response of the suspension in a much more complete manner than what was done previously, with e.g. shear reversal data. Such a model would enable a complete fluid mechanical model for suspensions, allowing to simulate and predict suspension flows in arbitrary geometries and flow conditions. This model would also be a basis and reference point to build richer models for more complex suspensions, e.g. for soft or adhesive particles.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Activities performed:

We setup discrete element simulations to characterize the mechanical response of dense non-Brownian suspensions of hard particles after flow changes, using the MD code LAMMPS. With this code, we simulated several flow changes: shear rotations (two successive simple shears where the flow direction is rotated about the flow gradient direction), simple shear followed by uniaxial extensions along 3 different axes, simple shear followed by bi-axial extension. This gave us data sets of hundreds of different flow changes, with full knowledge of the stress and microstructure response after flow changes. We performed these simulations at volume fractions ranging from semi-dilute (20% of the volume taken up by the particles), to very dense (58%).

We then turned to building a microstructure-informed constitutive model, using rational mechanics results about the allowed tensorial forms for such model, which is a standard approach. We used a recently introduced machine learning technique, called tensor-basis neural network, to identify the best models among the ones allowed according to rational mechanics, using part of our shear rotation data as the training set. The machine-learned model was then validated against flows mixing simple shear and extensional flows, revealing a model that is quantitative in all these cases, and outperforms the state-of-the-art model in the field (the 2018-2019 Gillissen-Wilson model). Moreover, using initial hints from the neural network model, we could learn a model devoid of neural network representation, that is, a model that can be fully and explicitly written on a piece of paper, only slightly less predictive power than the neural network model (still vastly outperforming the Gillissen-Wilson model).


Main achievement:
We resolved the long-standing problem of constitutive modeling of suspensions in its original formulation, with a pen-and-paper model.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The constitutive model we introduced will have a large impact because it is the central piece for fluid mechanics of suspensions. Because it is the first quantitative model for non-Brownian suspensions of hard particles, we expect the impact on application-related research will be significant. Our constitutive model should be readily usable in continuum fluid mechanics models and solvers, e.g. finite element solvers. This is the next step for us, given that the continuum-scale solvers are currently not our expertise. We will therefore look for collaboration with experts, mostly from applied mechanics, on this topic.