Study on binary collision of rod-like particles under simple shear flow
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Study on binary collision of rod-like 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 December 5, 2019; final revision received March 21, 2020; accepted June 6, 2020) In this study a theoretical study is carried out on the collision of two rod-like particles suspended in Newtonian fluid under a shear flow. The length of the particle is fixed at 2 m while the diameter is varied so that the aspect ratio (length/diameter) varies from 1 to 20. Liquid viscosity is changed from 0.01 to 1 Pa·s. The Brownian motion is considered to be negligible. Both hydrodynamic and van der Waals interactions are included in tracking the position and the orientation of each particle. The Hamaker constant is fixed at 1.06 × 1020 J. The result shows that the kinetic constant of coagulation is reduced to approximately 40% of the value for the non-interacting particles when the viscosity is 1 Pa·s. As collision modes, face-edge, side-side, side-edge and edge-edge are considered. The side-edge mode is most frequently observed in the given range of aspect ratio. Keywords: van der Waals interaction, hydrodynamic interaction, orientation distribution function, kinetic constant, collision mode, boundary integral method
Introduction Flows of suspensions of rod-like particles are important in many industries including fiber reinforced plastics processing and paper manufacturing (Sato et al., 1988; Akay and Barkley, 1991; Atic et al., 2005; Thomason 2009; Kouko et al., 2019). During the flow of a suspension, rodlike particles can be aggregated by collision of the particles and then the rheological properties of the suspension can change depending on the microstructure developed by the aggregation. Hence it is essential for proper processing of a suspension to understand the aggregation kinetics and the microstructure formation in the suspension of rod-like particles. Smoluchowski considered the collision of two noninteracting spheres of arbitrary sizes and derived the kinetic constant of the binary collision (Smoluchowski, 1918). Since then, several studies have been reported on the collision of two interacting spheres (Van de Ven and Mason, 1976; Zeichner and Schowalter, 1977; Higashitani et al., 1982). In the case of non-spherical particles, despite the practical importance, only a few theoretical studies have been reported (Philipse and Wierenga, 1998; Singh et al., 2011). Especially studies on the collision of interacting non-spherical particles have not been reported until the authors reported the coagulation of disk-like particles with hydrodynamic and van der Waals interactions recently (Lee and Kim, 2020a). In the report, they derived the general equation on the kinetic constant of the binary collision of non-spherical particles and devised a numerical algorithm to find out the time-independent orientation *Corresponding author; E-mail: [email protected]
© 2020 The Korean Society of R
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