Tangles, knots, and breakups of flexible fibres in turbulent fluids – NETFLEX

The dynamics of long flexible fibres in a turbulent flow involves multiple space and time scales and is the result of a complex interplay between their displacement, their deformation, and their interactions. Macroscopic fibres are present in several applications, such as the study of marine pollution by microplastics, the formation of long bacterial blooms in the oceans, and the flocculation of cellulose fibres in the paper industry. The dynamics of such elongated particles give rise to significantly more challenging questions than infinitesimal objects and are today at the centre of a strong interest in the experimental, numerical, and theoretical fluid dynamics communities.

We focus in this project on long, thin, flexible fibres suspended in a turbulent medium. Our aim is to understand and model the fragmentation and aggregation processes that they experience. We will bridge three levels of description. From a microscopic viewpoint, we will address how the fibers coupling with the surrounding viscous fluid affect internal stresses and interactions between several filaments. This will allow us to improve coarse-grained mesoscopic models to account for break-ups, contacts, knots, and entanglements, both within a single fibre and between several of them. This step will feed the development of macroscopic descriptions, which, in tandem with filtered turbulence models, will allow the study of long-term global evolutions in practical settings where inhomogeneities or anisotropies play a crucial role.

Our plan of action is organized into three axes. They combine the outcome of laboratory experiments, numerical simulations, and mathematical modelling, which reflects the specific expertise of the three partners.
The first part focuses on fragmentation processes, with the objective of answering several questions: How do fibres with sizes in the turbulent inertial range break up? What is the effect of their own inertia, and in particular of violent inertial waves? How to account for plastic effects?
The second aspect concerns the formation of fibre aggregates. Key questions that we will address are: How to describe the topology of knots and contacts from a statistical viewpoint? What are the mechanisms leading to aggregates? Do their size, shape, structure display universal properties? How is this changed when the fibers are active?
The third line of attack consists in developing large-scale models of turbulent fibre suspensions. Several issues will be tackled: How to design stochastic Lagrangian models of long objects that cope with the intricate turbulent space-time correlations? Can size evolution be described by population dynamics models with both aggregation and breakup? Can entangled fibres be properly described as a porous, deformable objects with an effective dynamics?

Experiments will be conducted at AMU in a newly built setup consisting of two arrays of high-speed jets that generate a homogeneous and isotropic turbulent flow inside a tank and in a rotor-strator cavity devoted to the study of anisotropic flows. High-speed cameras and a 3D reconstruction algorithm developed at AMU will be used to image the fibres. The numerical simulations will be based on a slender-body model of fibre and will consider two flow configurations: forced homogeneous isotropic turbulence and a bounded channel flow. The codes are available at UCA and are optimised for massive parallel servers. The mathematical modelling will rely on the expertise of the Inria team on stochastic analysis and population balance equations and will use in-house computational fluid dynamics (CFD) software.