Colloids and Surfaces A: Physicochem. Eng. Aspects 468 (2015) 87–94 Contents lists available at ScienceDirect Colloids and Surfaces A: Physicochemical and Engineering Aspects journa l h om epage: www.elsevier.com/locate/colsurfa Modeling particle-size distribution dynamics in a shear-induced breakage process with an improved breakage kernel: Importance of the internal bonds Feng Xiao a,b,∗ , Hui Xu a , Xiao-yan Li b , Dongsheng Wang a a State Key Laboratory of Aquatic Chemistry, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, 18 Shuangqing Road, Beijing 100085, China b Environmental Engineering Research Centre, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China h i g h l i g h t s • An improved particle breakage kernel has been developed. • Ratio of the bonding forces and shear forces regulates the breakage proba- bility. • Simulation results for the PSD evolu- tion compared well with the experi- mental results. • Hydrophobic bonding is stronger than van der Waals’ forces against shear breakage. • As the fractal dimension increases, the aggregates become stronger to shear breakage. g r a p h i c a l a b s t r a c t a r t i c l e i n f o Article history: Received 12 September 2014 Received in revised form 28 November 2014 Accepted 30 November 2014 Available online 11 December 2014 Keywords: Aggregate Bio-flocs Breakage kernel Fractal dimension Particle size distribution (PSD) a b s t r a c t An improved aggregate breakage kernel was developed that accounts for the effects of both the internal bonding forces between particles within an aggregate and the fluid shear stress exerted on the aggregate. The ratio of the two opposite forces regulates the probability of aggregate breakage. Using the improved breakage kernel, together with the sectional modeling technique, the dynamics of particle breakage induced by fluid shear was well simulated. The results show that the internal bonding forces determine the strength of the aggregates, and the hydrophobic bonding forces are much stronger than van der Waals’ forces for holding the aggregates against shear breakage. The simulations compared fairly well with the experimental results in terms of PSD evolution during the breakage of latex particle aggregates and activated sludge flocs. For the latex particle aggregates, van der Waals’ forces apparently are the main internal bonding force between particles. However, for activated sludge flocs, the non-DLVO hydrophobic forces are shown to play an important role in maintaining a stronger structure of the flocs. © 2014 Elsevier B.V. All rights reserved. ∗ Corresponding author at: State Key Laboratory of Aquatic Chemistry, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, 18 Shuangqing Road, Beijing 100085, China. Tel.: +86 10 62849138; fax: +86 10 62849138. E-mail addresses: fengxiao@rcees.ac.cn, xjtuxf@gmail.com (F. Xiao). 1. Introduction Flocculation, which aggregates smaller particles into larger ones, is a crucial step for many solid–liquid separation processes in water and wastewater treatment plants. Enlarging their size by flocculation can greatly facilitate the removal of particulate http://dx.doi.org/10.1016/j.colsurfa.2014.11.060 0927-7757/© 2014 Elsevier B.V. All rights reserved.