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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 $\mu_{eff}=(1+ \frac{5}{2} \lambda)\mu$. The second additional term derived is an effective active stress $\sigma_1$ that appears as a forcing term $\lambda \, \text{div} \, \sigma_1$ 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. 2022-04-11. Derivation of an effective rheology for dilute suspensions of micro-swimmers. https://arxiv.org/abs/2204.04967

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