Dynamic simulation of flexible fibers composed of linked rigid bodies

Abstract

A particle-level simulation method is employed to study the dynamics of flowing suspensions of rigid and flexible fibers. Fibers are modeled as chains of prolate spheroids connected through ball and socket joints. By varying the resistance in the joints, both flexible and rigid fibers can be modeled. Repulsive interactions between fibers are included, but hydrodynamic interactions and particle inertia are neglected in this implementation. The motion of a fiber is determined by solving the translational and rotational equations of motion for each spheroid. Simulations of isolated fibers in shear flow demonstrate that the method can reproduce known dynamical behavior of both rigid and flexible fibers. The transient behavior in the suspension relative viscosity under simple shear flow was also investigated. An oscillatory response similar to the experimental observations of Ivanov et al. was obtained for rigid fibers. Fiber flexibility reduced the period of oscillation, but had little effect on steady-state viscosities. These results verify that rigid and flexible fibers can be modeled with linked rigid prolate spheroids. Modeling fibers with fewer elongated bodies, as opposed to many spheres, significantly reduces computation time and facilitates the study of suspensions of many interacting, long fibers.

Buckling Instabilities and Complex Trajectories in a Simple Model of Uniflagellar Bacteria

“…Affixed to each segment is a local coordinate system as demonstrated by Ross et al (21). Any orientation in ℝ 3 can be represented by four Euler parameters, q ij (i ¼ b; f and j ¼ 0; 1; 2; 3), that explicitly define transformations between different frames of reference, via rotation matrices R i ,…”

Simulation of single fiber dynamics

“…This model eliminates the need for iterative constraints to maintain fiber connectivity, and can represent large-aspect ratio fibers with relatively few bodies. These features help to reduce computations, facilitating simulation of concentrated suspensions 1 .…”

“…Many previous investigations of fiber dynamics, both experimental and theoretical, have focused on the dynamics of rigid fibers, while relatively little attention has been paid to the more complicated dynamics of flexible fibers. In a previous paper 1 , we presented a mechanical model for flexible fibers and a simulation technique for studying their dynamics in flowing suspensions. The purposes of this paper are to verify that the model and simulation method accurately reproduce a wide variety of theoretical predictions and experimental observations of isolated rigid and flexible fiber dynamics, and to illustrate some of the complicated dynamics of flexible fibers.…”

Dynamics of a flexible fibre in a sheared two-dimensional foam: Numerical simulations

“…Also, since the pioneering theoretical works of Jeffery (1922) on the dynamics of ellipsoidal particles, the study of fibres in Newtonian fluid flows has been the subject of many experimental and numerical studies, with motivations as diverse as papermaking, water 40 purification, dynamics of DNA molecules or microswimmers (Forgacs and Mason, 1959;Yamamoto and Matsuoka, 1996;Ross and Klingenberg, 1997;Switzer and Klingenberg, 2003;Subramanian and Koch, 2005;Gauger and Stark, 2006;Lindström and Uesaka, 2007;Wandersman et al, 2010;Lindner and Shelley, 2015;Farutin et al, 2016). In particular, fibre suspensions have often been mod-45 elled by studying the interactions between a laminar simple shear or Poiseuille flow and flexible rods modelled as strings of spherical (or circular) beads.…”