Minimal model for a hydrodynamic fingering instability in microroller suspensions

Blaise Delmotte, Aleksandar Donev, Michelle Driscoll, Paul Chaikin

Research output: Contribution to journalArticle

3 Scopus citations

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, Nat. Phys. 13, 375 (2017)10.1038/nphys3970]. 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.

Original languageEnglish (US)
Article number114301
JournalPhysical Review Fluids
Volume2
Issue number11
DOIs
StatePublished - Nov 2017

ASJC Scopus subject areas

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

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