Modeling of Floc Forming Suspensions Coupling the Population Balance Equation for Floc Aggregation-Breakage and the White-Metzner Model

抄録

A viscoelastic model for floc-forming suspensions considering the aggregation and breakage of flocs during flows was developed based on our previous model, in which a population balance equation was adopted to simulate the floc aggregation-breakage. Similarly to the previous model, a Krieger-Dougherty model was used to describe the dependence of viscosity on the volume fraction of flocs, and a White-Metzner type model was used to represent the effect of viscoelasticity. In addition, the dependence of the relaxation time on the volume fraction of flocs was introduced to the present model using an elastic modulus function that depends on the effective volume fraction of flocs. The rheological behavior of the present model was examined by performing the simulation of startup flows of simple shear. The results of the simulation indicated that the temporal change in the distribution of floc size greatly depended on the elastic modulus function. The temporal behavior of the first normal stress difference therefore exhibits differences just after the startup of flow, depending on the elastic modulus function. The present model will be a simple viscoelastic constitutive model for floc-forming suspensions that represents the dependence of both viscosity and relaxation time on the floc size distribution.