2021 Volume 49 Issue 3 Pages 207-213
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 df. The present study considered the effect of df 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 df and shows a shear-thinning property, which appears more strongly with deceasing df. The first normal stress coefficient shows fractal-dimension dependence and is larger for smaller df. These phenomena are relevant to a characteristic of the present model whereby the effective volume fraction is larger for suspensions of flocs of smaller df. 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.
