### Abstract

A general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to $N$-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity [{\μ}] increases monotonically when the distance H between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a 'weakly confined' regime (for H>l, where l is the particle length), where [{\μ}] is slightly larger for smaller H; (ii) a 'semi-confined' regime, when H becomes smaller than l, where [{\μ}] rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a 'strongly confined' regime when H becomes smaller than 2-3 particle widths d, where [{\μ}] rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5-6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

Original language | English |
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Pages (from-to) | 133-147 |

Number of pages | 15 |

Journal | Journal of Fluid Mechanics |

Volume | 764 |

DOIs | |

State | Published - Dec 23 2014 |

### Keywords

- complex fluids
- low-Reynolds-number flows
- suspensions

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## Cite this

*Journal of Fluid Mechanics*,

*764*, 133-147. https://doi.org/10.1017/jfm.2014.690