3 research outputs found
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.Comment: 64 page
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 . The second additional term derived is an effective
active stress that appears as a forcing term in the fluid equation. We then investigate the effects of this
term depending on the micro-swimmers nature and their distribution in the
fluid.Comment: 32 pages, 2 figure