Modeling the intrinsic viscosity of polydisperse disks

Issam Ismail, Jeremy Vandenberg, Ahmed Abdala, Chris Macosko

Research output: Contribution to journalArticle

Abstract

In this work, we model the rheology of dilute colloidal oblate spheroids in their high aspect ratio limit of circular disks. Theoretical models for the intrinsic viscosity, [η], of disks in shear flow are reviewed: The shear-independent, monodisperse Kuhn-Kuhn model, its polydisperse form by van der Kooij, and the shear-dependent models of Stewart and Sorenson, Leal and Hinch, and Brenner. Based on these previous works, three analytical models are introduced to describe the shear response over the entire range of practically accessible rotational Peclet numbers (Pe) and aspect ratios. Using the fact that [η] is linearly additive for sufficiently dilute systems we derive a general expression for polydisperse disks as a function of the two independent variables of particle diameter D and thickness t, that is, assuming D and t to be uncorrelated independent variables. We then argue for continuum modeling being preferable to discrete for using rheological measurements to estimate particle size distribution parameters. Computational results are shown for the continuum model in shear flow and generalized to uniaxial and planar extension, as well as to different particle distributions such as lognormal, normal, and bimodal. Finally, a modified form of [η], which we describe as innate viscosity (η), is suggested as an alternative method of modeling rheology of dilute dispersions.

Original languageEnglish
Pages (from-to)997-1006
Number of pages10
JournalJournal of Rheology
Volume61
Issue number5
DOIs
Publication statusPublished - 1 Sep 2017

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Viscosity
viscosity
Shear flow
Rheology
Aspect ratio
shear
rheology
shear flow
continuum modeling
Peclet number
oblate spheroids
Dispersions
Particle size analysis
Analytical models
high aspect ratio
particle size distribution
aspect ratio
continuums
estimates

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Modeling the intrinsic viscosity of polydisperse disks. / Ismail, Issam; Vandenberg, Jeremy; Abdala, Ahmed; Macosko, Chris.

In: Journal of Rheology, Vol. 61, No. 5, 01.09.2017, p. 997-1006.

Research output: Contribution to journalArticle

Ismail, I, Vandenberg, J, Abdala, A & Macosko, C 2017, 'Modeling the intrinsic viscosity of polydisperse disks', Journal of Rheology, vol. 61, no. 5, pp. 997-1006. https://doi.org/10.1122/1.4996843
Ismail, Issam ; Vandenberg, Jeremy ; Abdala, Ahmed ; Macosko, Chris. / Modeling the intrinsic viscosity of polydisperse disks. In: Journal of Rheology. 2017 ; Vol. 61, No. 5. pp. 997-1006.
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