arXiv subjects

Alexandre Girodroux-Lavigne

Publications and source records attributed to Alexandre Girodroux-Lavigne.

3 recordsLinked to original sources

arXiv2025

Hydrodynamic limit of multiscale viscoelastic models for rigid particle suspensions

We study the multiscale viscoelastic Doi model for suspensions of Brownian rigid rod-like particles, as well as its generalization by Saintillan and Shelley for self-propelled particles. We consider the regime of a small Weissenberg number, which corresponds to a fast rotational diffusion compared to the fluid velocity gradient, and we analyze the resulting hydrodynamic approximation. More precisely, we show the asymptotic validity of macroscopic nonlinear viscoelastic models, in form of so-called ordered fluid models, as an expansion in the Weissenberg number. The result holds for zero Reynolds number in 3D and for arbitrary Reynolds number in 2D. Along the way, we establish several new well-posedness and regularity results for nonlinear fluid models, which may be of independent interest.

math.AP↗

arXiv2022

Derivation of an effective rheology for dilute suspensions of micro-swimmers

We provide a rigorous derivation of an effective rheology for dilute viscous suspensions of self-propelled particles. We derive at the limit an effective Stokes system with two additional terms. The first term corresponds to an effective viscosity that matches the famous Einstein's formula $μ_{eff}=(1+ \frac{5}{2} λ)μ$. The second additional term derived is an effective active stress $σ_1$ that appears as a forcing term $λ\, \text{div} \, σ_1$ in the fluid equation. We then investigate the effects of this term depending on the micro-swimmers nature and their distribution in the fluid.

math.AP↗

arXiv2021

Homogenization of stiff inclusions through network approximation

We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the inter-particle distance, an effective model with finite homogeneous conductivity exists. Relying on ideas from network approximation, we provide a relaxed criterion ensuring homogenization. Several examples not covered by the previous theory are discussed.

math.AP↗