Effect of Fractal Dimension of Floc Size in a Constitutive Model Based on a Population Balance Equation for Floc-Forming Suspensions on Shear Rheology

• Yamamoto Takehiro

  Department of Mechanical Engineering, Osaka Electro-Communication University

Bibliographic Information

Other Title

• Effect of Fractal Dimension of Floe Size in a Constitutive Model Based on a Population Balance Equation for Floc-Forming Suspensions on Shear Rheology

Abstract

A viscoelastic constitutive model for floc-forming suspensions developed in a previous study couples a population balance equation for the floc aggregation-breakage and a White-Metzner-type viscoelastic model. In the White-Metzner model, the viscosity and the relaxation time were respectively represented by a Krieger-Dougherty model and a power-law model, which depend on the effective volume fraction of flocs. The relation between the effective floc radius and the length of a monomer, which is the minimum unit of a fiber, was described using the mass to radius fractal dimension d_f. The present study considered the effect of d_f on the rheological properties of the proposed model and analyzed its shear property by simulating startup shear flows. The steady shear viscosity is larger for suspensions of smaller d_f and shows a shear-thinning property, which appears more strongly with deceasing d_f. The first normal stress coefficient shows fractal-dimension dependence and is larger for smaller d_f. These phenomena are relevant to a characteristic of the present model whereby the effective volume fraction is larger for suspensions of flocs of smaller d_f. Furthermore, analyses of the transient behavior of shear rheology revealed that the change in the floc size distribution proceeded in a much shorter time as compared to the relaxation time λ of the White-Metzner model, and hence the growth of macroscopic properties, such as shear viscosity and the first normal stress coefficient, was mainly dominated by the steady-state value of λ, although it depends on temporal change in the floc size distribution of flocs.

Journal

• Nihon Reoroji Gakkaishi

  Nihon Reoroji Gakkaishi 49 (3), 207-213, 2021-06-15

  The Society of Rheology, Japan

Keywords

• Fiber flocs
• Population balance equation
• Fractal dimension
• Effective volume fraction
• Shear rheology

Details

• CRID: 1390288701067602688
• NII Article ID: 130008065175
• NII Book ID: AN00198812
• DOI: 10.1678/rheology.49.207
• ISSN: 21864586
• ISSN: 03871533
• NDL BIB ID: 031575259
• Web Site: http://id.ndl.go.jp/bib/031575259
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I031575259
• Web Site: https://www.jstage.jst.go.jp/article/rheology/49/3/49_207/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed