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

Alexandre Girodroux-Lavigne

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arXiv · 2204.04967

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

Alexandre Girodroux-Lavigne

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Abstract

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.

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Alexandre Girodroux-Lavigne. 2022-09-07. Derivation of an effective rheology for dilute suspensions of micro-swimmers. https://arxiv.org/abs/2204.04967

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