Collective viscous propulsion of a two-dimensional flotilla of Marangoni boats
File(s)
Accepted version
Author(s)
Crowdy, Darren
Type
Journal Article
Abstract
A closed-form solution is presented for the collective Marangoni-induced motion of a two-dimensional periodic array, or “flotilla”, of Marangoni boats on deep water at zero Reynolds, capillary and surface P´eclet numbers. The physical set-up is identical to the model of Marangoni propulsion proposed by Lauga & Davis [J. Fluid Mech., 705, (2012)] but accounts now for interaction effects between boats, and in a simpler two-dimensional setting. The boats are modelled as identical thin floating strips each self-actuated by a trailing edge surfactant source that lowers the surface tension there according to a linear equation of state. The collective Marangoni propulsion speed of a flotilla of boats is found to be (2πµδ) −1∆σ log sec(πδ/2) where δ is the meniscus coverage fraction, µ is the subphase fluid viscosity and ∆σ is the surfactant-induced surface tension disparity across each boat. The theoretical result exemplifies the mechanism for collective rectilinear motion due to Marangoni convection caused by the diffusion of insoluble surfactant.
Keywords: Marangoni boat, camphor boat, viscous propulsion, active particle.
Keywords: Marangoni boat, camphor boat, viscous propulsion, active particle.
Date Issued
2020-12-21
Date Acceptance
2020-11-12
Citation
Physical Review Fluids, 2020, 5, pp.124004 – 1-124004 – 17
ISSN
2469-990X
Publisher
American Physical Society
Start Page
124004 – 1
End Page
124004 – 17
Journal / Book Title
Physical Review Fluids
Volume
5
Copyright Statement
© 2020 American Physical Society.
Identifier
https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.5.124004
Subjects
Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics
SELF-PROPELLED OBJECTS
FLOW
SURFACTANT
MOTION
WATER
0102 Applied Mathematics
0203 Classical Physics
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2020-12-21