Minimal model for a hydrodynamic fingering instability in microroller suspensions

Blaise Delmotte, Aleksandar Donev, Michelle Driscoll, and Paul Chaikin
Phys. Rev. Fluids 2, 114301 – Published 10 November 2017

Abstract

We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [M. Driscoll et al., Nat. Phys. 13, 375 (2017)]. Our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamic interactions and reproduces the length-scale selection observed in large-scale particle simulations and in experiments. By adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations and qualitative agreement with experimental measurements. Our linear stability analysis indicates that this instability is caused by the combination of the advective and transverse flows generated by the microrollers near a no-slip surface. Our simple model offers an interesting formalism to characterize other hydrodynamic instabilities that have not been well understood, such as size scale selection in suspensions of particles sedimenting adjacent to a wall, or the recently observed formations of traveling phonons in systems of confined driven particles.

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  • Received 23 June 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.114301

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Blaise Delmotte* and Aleksandar Donev

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA

Michelle Driscoll and Paul Chaikin

  • Department of Physics, New York University, New York, New York 10003, USA

  • *delmotte@courant.nyu.edu

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Issue

Vol. 2, Iss. 11 — November 2017

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