A method for dynamic simulation of rigid and flexible fibers in a flow field

Abstract

A method is proposed for simulating the dynamic behavior of rigid and flexible fibers in a flow field. The fiber is regarded as made up of spheres that are lined up and bonded to each neighbor. Each pair of bonded spheres can stretch, bend, and twist, by changing bond distance, bond angle, and torsion angle between spheres, respectively. The strength of bonding, or flexibility of the fiber model, is defined by three parameters of stretching, bending, and twisting constants. By altering these parameters, the property of the fiber model can be changed to be rigid to flexible. The motion of the fiber model in a flow field is determined by solving the translational and rotational equations for individual spheres under the hydrodynamic force and torque exerting on. This method was applied to simulate rotational motions with and without bending deformation of the fiber in a simple shear flow under the conditions of infinitely dilute system, no hydrodynamic interaction and low Reynolds number of a particle. For the rigid fiber, the computed period of rotation and the computed distribution of orientation angle agree with those calculated by Jeffery’s equation with an equivalent ellipsoidal aspect ratio. For the flexible fiber, the period of rotation decreases rapidly with the growth of bending deformation of the fiber and rotation orbits deviate from a circular one of the rigid fiber. These tendencies are similar to experimental ones described by Forgacs and Mason. These results show that the proposed method using bonded spheres’ model can reproduce the dynamic behavior of rigid and flexible fibers in a flow field successfully.