Thèse Modélisation Multiéchelle du Transport de Particules de Taille Finies dans des Gels Fibreux Inspirés de Biomatériaux H/F - Doctorat.Gouv.Fr

Établissement : Université Paris-Saclay GS Sciences de l'ingénierie et des systèmes École doctorale : Sciences Mécaniques et Energétiques, Matériaux et Géosciences Laboratoire de recherche : EM2C - Energétique Moléculaire et Macroscopique, Combustion Direction de la thèse : Aymeric VIÉ ORCID 0000000339980862 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-04-21T23:59:59 Les milieux poreux fibreux sont omniprésents dans de nombreuses applications technologiques (filtres, isolants, hydrogels pour l'administration de médicaments, textiles...) ainsi qu'en biologie (collagène dans les tissus vivants, cytosquelette intracellulaire...). Grâce à leur porosité, ils permettent divers mécanismes de transferts en leur sein (espèces chimiques, chaleur, flux, etc.), tout en conservant leur intégrité mécanique. Il est donc important de développer des approches de modélisation permettant de prédire les performances de ces matériaux fibreux.

Nous avons récemment montré que la diffusion des macromolécules dans les gels biologiques pouvait être bien décrite par des approches de modélisation des milieux poreux, à condition de tenir compte de trainée hydrodynamique entravant la diffusion [Destrian2026]. Ce mécanisme corrige la relation de Stokes-Einstein pour tenir compte de la perméabilité du gel. Cependant, le mécanisme à l'échelle des pores responsable de cet effet et sa relation avec l'expression semi-empirique de la trainée hydrodynamique sont mal compris.

Ce projet vise à établir un modèle physique cohérent de la diffusion des macromolécules dans les gels bioinspirés à partir de la physique à l'échelle des pores, et à mettre à l'échelle le système afin d'obtenir les équations de transport pertinentes à l'échelle macroscopique du continuum.
The challenge related to the modeling of molecule transport in gels is a consequence of the separation of scales between the polymer pore scale (~10-100nm) and the equivalent continuous gel scale (>1µm). At the pore scale, the system can be thought of as a fibrous porous medium made of interwoven polymer chains, where transport phenomena are functions of network density, anisotropy, fiber thickness and stiffness, and the relative size of the transported molecules. The fibers can be considered as solid obstacles to fluid flow and molecule diffusion. For molecules and proteins of few nanometers, some transport related effects cannot be accounted for within the continuum mechanics framework because the particle size is not negligible compared to the obstacle size. This challenges the validity of current coarse-grain models at the macroscopic scale.

Some empirical transport equations have been proposed in the field of polymer-physics. Notably, the hydrodynamic drag model has been used to correct the diffusivity for the relative particles to pore size [Johnson1996]. It is worth noting that the basis of this model was originally derived in the context of transport in porous media [Brinkman1947]. However, in polymer gel, the justification and limit of validity of the hydrodynamic drag model at the gel-scale remain disconnected from the pore-scale physics.

Several biological materials can also be considered as gels. For instance, the intracellular medium is often described as a crowded environment where organelles are embedded in a fibrous cytoskeleton gel-like structure. Our team previously showed that passive diffusion of globular macromolecules in the intracellular space can be correctly predicted at the cell scale (~10µm) using a porous medium description [Destrian2026]. The two key elements of this model were (i) to consider multiplicative effects between tortuosity and hydrodynamic drag in the diffusional reduction, and (ii) to apply an upscaling procedure to obtain the effective cell-scale diffusivity. The model diffusivity predicted very well the experimental measurement of GFP diffusivity in live cells across various intracellular crowding conditions. However, the pore-scale physical origin of the hydrodynamic drag effect and the justification of its multiplicative effect with tortuous diffusional hindrance remains to be proven. The main objective of the project is to develop a combined numerical and theoretical approach that bridges the particle transport at the pore scale to the macroscopic equations. We aim to rigorously justify the current form of hydrodynamic diffusional hindrance commonly used empirically in hydrogels and identify possible corrective terms.

The project will be conducted in two stages, first focusing on the pore scale, then on the upscaling to the macroscopic scale.

At the pore scale, the mode of particle diffusion in fibrous porous media will account for the coupling between particles, fibers, and hydrodynamics. This model will allow us to compute statistics on the particle trajectory and determine its effective diffusion coefficient as a function of the fibrous structure property. Specifically, we will
a) enhance our current fibrous structure generator to produce hydrogel-like fibrous structures, based on physical considerations such as fiber stiffness, anisotropy, contact types, and attractive/repulsive forces
b) adapt a Brownian diffusion model of particle compatible with the generated fiber geometries
c) couple the above modules to a fluid flow solver using the immerged boundary method
d) compute the effective diffusion coefficient of particles in fibrous media and compare them with experimental literature

Then, an upscaling procedure will be conducted to obtain the gel-scale transport equations and its effective properties. Indeed, to obtain a practical coarse-grain transport equation, non-essential information at the pore-scale must be filtered out through a formal upscaling approach. Statistical ensembles of the pore scale will be considered to obtain a continuous description that can be homogenized using the method of volume averaging [Whitaker1999, Chabanon2015, Chabanon2026]. The resulting coarse-grain model will allow us to formally determine the contribution of local hydrodynamic drag and pore tortuous hindrance at the gel-scale.

Depending on the candidate profile, experiments to measure the particle diffusivity in gels will be considered in collaboration with teams specialized in hydrogel (Hervé Duval, laboratoire LGPM, CentraleSupélec), and biological gels (Arthur Molines, I2BC, Université Paris-Saclay).

Étudiant titulaire d'un diplôme de niveau master dans le domaine de la mécanique des fluides, de l'ingénierie mécanique, mathématiques appliquées, ou matière molle. De l'intéret pour la biophysique est un plus mais n'est pas obligatoire. De bonne compétences de communication en anglais sont importantes.