Viscosity of dilute suspensions of rodlike particles: A numerical simulation method

Abstract

The recently developed simulation method, named as the particle simulation method (PSM), is extended to predict the viscosity of dilute suspensions of rodlike particles. In this method a rodlike particle is modeled by bonded spheres. Each bond has three types of springs for stretching, bending, and twisting deformation. The rod model can therefore deform by changing the bond distance, bond angle, and torsion angle between paired spheres. The rod model can represent a variety of rigidity by modifying the bond parameters related to Young’s modulus and the shear modulus of the real particle. The time evolution of each constituent sphere of the rod model is followed by molecular‐dynamics‐type approach. The intrinsic viscosity of a suspension of rodlike particles is derived from calculating an increased energy dissipation for each sphere of the rod model in a viscous fluid. With and without deformation of the particle, the motion of the rodlike particle was numerically simulated in a three‐dimensional simple shear flow at a low particle Reynolds number and without Brownian motion of particles. The intrinsic viscosity of the suspension of rodlike particles was investigated on orientation angle, rotation orbit, deformation, and aspect ratio of the particle. For the rigid rodlike particle, the simulated rotation orbit compared extremely well with theoretical one which was obtained for a rigid ellipsoidal particle by use of Jeffery’s equation. The simulated dependence of the intrinsic viscosity on various factors was also identical with that of theories for suspensions of rigid rodlike particles. For the flexible rodlike particle, the rotation orbit could be obtained by the particle simulation method and it was also cleared that the intrinsic viscosity decreased as occurring of recoverable deformation of the rodlike particle induced by flow.