Coagulation kinetics of round-sided disk particles under simple shear flow
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Coagulation kinetics of round-sided disk particles under simple shear flow Hyun Seop Lee and Chong Youp Kim* Department of Chemical and Biological Engineering, Korea University, Seoul 02841, Republic of Korea (Received November 9, 2019; final revision received February 7, 2020; accepted March 20, 2020) In this study a theoretical study is carried out on the binary collision of round-sided disks (RSD) suspended in a Newtonian fluid under a simple shear flow. RSD is composed of a disk part and a half-torus part which circumscribes the side of the disk. The diameter of the disk is fixed at 2 m while the thickness and the half-torus size are varied so that the aspect ratio varies from 0.13 to 0.288. The liquid viscosity is changed from 0.01 to 1 Pa·s. The hydrodynamic force and van der Waals force with the Hamaker constant of 1.06 × 1020 J are considered in tracking the position and the orientation of each particle. The Brownian motion is considered to be negligible. The collision of two particles initially separated by sufficiently a long distance is considered and the kinetic constant of coagulation is obtained by considering the presence of collision, the orientations of two particles and the flux of liquid flow. The result shows that the kinetic constant of coagulation is reduced to approximately 1/4 of the kinetic constant of non-interacting particles by the hydrodynamic interaction when the viscosity is 1 Pa·s. As collision modes, side-side and side-edge are considered. Side-side mode is found to be the dominant mode of collision for differing aspect ratio and differing viscosity of the liquid. The dominance of the side-side collision mode implies the formation of two-dimensional flocs in the shear flow. Keywords: binary collision, kinetic constant, van der Waals interaction, hydrodynamic interaction, collision mode
Introduction Aggregation of particles suspended in flowing liquids is of great interest in many industries including paper manufacturing, water purification, coating and so on (Bai et al., 2009; Fukasawa and Adachi, 2006; Jarvis et al., 2006; Jin and Speers, 1998; Mihara 2009; Rodrigues and Rubio, 2007; Yu et al., 2010). When particles are aggregated in a suspension, a microstructure can be developed in the suspension and the rheological properties of the suspension can be changed with the development of the microstructure. Recently, the authors reported the formation of twodimensional (2D) flocs in the suspension of tungsten disulfide plate-like particles in polybutene under a simple shear flow (Lee and Kim, 2018). They also reported the change of viscosity with the development of the microstructure. The present study is a continuation of their work to understand the mechanism of the formation of 2D flocs. Since the pioneering work of Smoluchowski (1918) on the coagulation of two spherical, non-interacting particles, several studies have been reported on the collision of two spheres with colloidal and hydrodynamic interactions. Despite of practical importance, most of the t
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