Minimal model for a hydrodynamic fingering instability in microroller suspensions

Blaise Delmotte, Aleksandar Donev, Michelle Driscoll, Paul Chaikin

Research output: Contribution to journalArticle

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 1 2017

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Hydrodynamic Instability
Minimal Model
Suspensions
Hydrodynamics
Hydrodynamic Interaction
Phonons
Line
Linear Stability Analysis
Continuum Model
Dispersion Relation
Length Scale
Slip
Linear stability analysis
Simulation
Transverse
Adjacent
Model
Experiment
Experiments

ASJC Scopus subject areas

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

Cite this

Minimal model for a hydrodynamic fingering instability in microroller suspensions. / Delmotte, Blaise; Donev, Aleksandar; Driscoll, Michelle; Chaikin, Paul.

In: Physical Review Fluids, Vol. 2, No. 11, 114301, 01.11.2017.

Research output: Contribution to journalArticle

Delmotte, Blaise ; Donev, Aleksandar ; Driscoll, Michelle ; Chaikin, Paul. / Minimal model for a hydrodynamic fingering instability in microroller suspensions. In: Physical Review Fluids. 2017 ; Vol. 2, No. 11.
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