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Interactions and grouping behaviours of microswimmers and spheres

Published online by Cambridge University Press:  04 November 2025

Deming Nie Open the ORCID record for Deming Nie [Opens in a new window] ,
Zenan Lai ,
Kai Zhang  and
Jianzhong Lin Open the ORCID record for Jianzhong Lin [Opens in a new window]
Deming Nie
Affiliation:
College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, PR China
Zenan Lai
Affiliation:
College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, PR China
Kai Zhang
Affiliation:
College of Metrology Measurement and Instrument, China Jiliang University, Hangzhou, PR China
Jianzhong Lin*
Affiliation:
Key Laboratory of Impact and Safety Engineering, Ministry of Education, Ningbo University, Ningbo, PR China State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, PR China
*
Corresponding author: Jianzhong Lin, mecjzlin@zju.edu.cn
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Abstract

We performed three-dimensional simulations to study the motion and interaction of microswimmers (pulling- and pushing-type squirmers) and spheres for Reynolds numbers ranging from 0.01 to 1 under conditions in which all particles were axially aligned with each other. We show that pullers are attractive and pushers are repulsive, in terms of the pressure at the front and rear of the squirmers. Correspondingly, the pullers always come close to each other and form a string that swims slightly faster than does a single puller. A possible reason for this finding is discussed. In contrast, whether a leading puller touches a trailing pusher depends primarily on its strength. When the two have similar strengths, they come into contact and form a stable doublet with finite inertia. The speed of the doublet is substantially higher than that of a single pusher owing to the additional force stemming from the fore and aft pressure differences of the doublet. We also demonstrate how a leading pusher interacts with a trailing puller, which is quite different. In contrast, a sphere can be directly or hydrodynamically ‘pushed’ to run by a puller or a pusher. In particular, we reveal that the sphere exhibits the highest speed when ‘pulled’ by a leading puller and ‘pushed’ by a trailing pusher simultaneously. Grouping behaviours reflect the interacting nature of the microswimmers and spheres from different aspects. A bunch of pushers/pullers eventually appears in pairs or forms a string depending on the Reynolds number, similar to groups of pushers/spheres and pullers/spheres.

JFM classification

Complex Fluids: Active matter Low-Reynolds-number flows: Low-Reynolds-number flows

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1022 , 10 November 2025 , A37
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Nie et al. supplementary movie 1

Interaction between two identical pullers (β1 = β2 = 5) at Res = 0.01.
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File 354.1 KB
Supplementary material: File

Nie et al. supplementary movie 2

Interaction between two identical pullers (β1 = β2 = 5) at Res = 0.01.
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File 817.8 KB
Supplementary material: File

Nie et al. supplementary movie 3

Interaction between two identical pullers (β1 = β2 = 5) at Res = 1.
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File 588.8 KB
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Nie et al. supplementary movie 4

Interaction between a leading puller (β2 = 5) and a trailing pusher (β1 = -5) at Res = 0.01.
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Nie et al. supplementary movie 5

Interaction between a leading puller (β2 = 5) and a trailing pusher (β1 = -5) at Res = 0.1.
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File 1.1 MB
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Nie et al. supplementary movie 6

Interaction between a leading puller (β2 = 5) and a trailing pusher (β1 = -5) at Res = 1.
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File 725 KB
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Nie et al. supplementary movie 7

Interaction between a leading sphere and a trailing pusher (β = -5) at Res = 1.
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File 508.3 KB
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Nie et al. supplementary movie 8

Interaction between a leading sphere and a trailing puller (β = 5) at Res = 1.
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Nie et al. supplementary movie 9

Motion of a sphere between a leading puller (β = 5) and a trailing pusher (β = -5) at Res = 0.1.
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Nie et al. supplementary movie 10

Motion of a sphere leading a trailing puller (β = 5) and a trailing pusher (β = -5) at Res = 0.1.
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Nie et al. supplementary movie 11

Formation of a string consisting of five pullers (β = 5) at Res = 1.
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Nie et al. supplementary movie 12

Formation of a string consisting of six pullers (β = 5) at Res = 1.
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File 794.4 KB
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Nie et al. supplementary movie 13

Grouping behavior of an array (six particles) of puller-pusher at Res = 1.
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Nie et al. supplementary movie 14

Grouping behavior of an array (five particles) of puller-pusher at Res = 0.1.
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Nie et al. supplementary movie 15

Grouping behavior of an array (four particles) of pusher-sphere at Res = 1.
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Nie et al. supplementary movie 16

Grouping behavior of an array (four particles) of puller-sphere at Res = 1.
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