Collective surfing of two self-propelled swimmers at liquid-air interface aided by self-induced Marangoni flow

Prajitha Mottammal, Sumesh P. Thampi, and Andrey Pototsky
Phys. Rev. Fluids 6, 094004 – Published 28 September 2021
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Abstract

We report a closed analytical form of two types of linearly unstable rotational equilibria for a planar motion of two hydrodynamically coupled, inertia-free, pusher swimmers in the bulk of a fluid and at a planar, stress-free, fluid interface. Both types correspond to a periodic motion of pushers along circular trajectories with a constant angular velocity in such a way that the distance between the pushers and their relative orientation remain constant. The first orbit type represents the motion along a common circle, when each pusher makes a 35.2 angle with their relative position vector. In the second type of orbiting, the pushers move along circles of different radii while the orientation vectors of the pushers make 20.90 and 110.90 angles with their relative position vector. The first orbit type is monotonically unstable and the second orbit type is oscillatorily unstable. Next we show that both types of equilibria can be stabilized by self-induced Marangoni flow, generated by two pushers bound to move along a planar liquid-air interface. Neglecting inertia, we couple the motion of pushers with the advection-diffusion equation for the concentration of an insoluble surfactant, produced by the swimmers. The surfactant is assumed to homogeneously decompose at a constant rate. Numerical simulations in the regime of nonzero Peclet number reveal the existence of stable periodic orbits that are directly linked to the unstable equilibria found analytically in the absence of the Marangoni flow.

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  • Received 27 May 2021
  • Accepted 16 September 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.094004

©2021 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Prajitha Mottammal1, Sumesh P. Thampi1, and Andrey Pototsky2,*

  • 1Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India
  • 2Department of Mathematics, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

  • *apototskyy@swin.edu.au

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Issue

Vol. 6, Iss. 9 — September 2021

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