Structure and breakup of flocs subjected to fluid stresses: II. Theory

Abstract

An improved model for the breakup of an isolated floc in a shear flow is developed, similar in concept to previous versions but generalized to consider a spatial variation of the internal volume fraction of the form ϕ ∝ r D−3 . Assumptions of linear elasticity and the Mises criterion for yield, with moduli and critical stress varying with volume fraction as φ n , produce a relationship between floc radius R and shear rate γ of the form R ∼ γ (D−1) 2n(D−3) in the nondraining limit. Our experimental results for floc breakup are correlated with D = 2.48 and n = 4.45, in good agreement with independent measures of D from the floc mass and n from the elasticity of flocculated networks. The maximum strain at rupture is estimated to be ∼5%, in accord with the limit of linearity in the elasticity experiments. More general theoretical results are also presented to facilitate comparison with future experiments.