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Interaction network analysis in shear thickening suspensions

Marcio Gameiro1,2,*, Abhinendra Singh3,4,5,†, Lou Kondic6,‡, Konstantin Mischaikow2,§, and Jeffrey F. Morris3,7,∥

  • 1Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil
  • 2Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA
  • 3Benjamin Levich Institute, CUNY City College of New York, New York, New York 10031, USA
  • 4Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
  • 5James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
  • 6Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
  • 7Department of Chemical Engineering, CUNY City College of New York, New York, New York 10031, USA

  • *gameiro@icmc.usp.br
  • †asingh.iitkgp@gmail.com
  • ‡Corresponding author: kondic@njit.edu
  • §mischaik@math.rutgers.edu
  • ∥morris@ccny.cuny.edu
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Phys. Rev. Fluids 5, 034307 – Published 23 March, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.034307

Abstract

Dense frictional particulate suspensions in a viscous liquid undergo increasingly strong continuous shear thickening as the solid packing fraction, ϕ, increases above a critical volume fraction, and discontinuous shear thickening is observed for even higher packing fractions. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress, with the transition determined by overcoming a repulsive force. The rheology and networks of frictional forces from two- and three-dimensional simulations of shear-thickening suspensions are studied. These are analyzed using measures of the topology of the network, including tools of persistent homology. We observe that at low stress, the frictional interaction networks are predominantly quasilinear along the compression axis. With an increase in stress, the force networks become more isotropic, forming loops in addition to chainlike structures. The topological measures of Betti numbers and total persistence provide a compact means of describing the mean properties of the frictional force networks, and provide a link between macroscopic rheology and the microscopic interactions. A total persistence measure describing the significance of loops in the force network structure, as a function of stress and packing fraction, shows behavior similar to that of relative viscosity, and displays a scaling law near the jamming fraction for both two- and three-dimensional systems considered. The total persistence measures for both dimensions are found to be very similar.

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Outline

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Phys. Rev. Fluids 5, 034307– Published 23 March, 2020
  • Received 13 March 2019
  • Accepted 18 February 2020
Article part of CHORUS
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