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.

Modelling percolation in fibre and sphere mixtures: Routes to more efficient network formation

“…So, in a fixed external field, the longer fibres will experience higher dipole moment than shorter fibres, and hence may be expected to show higher alignment, which is qualitatively consistent with our simulation results, although the real difference in orientation due to a change in aspect ratio is likely to be even greater. Previous work modelling fibres under shear [47] and analysing conducting rods in electric fields [48] reports similar trends. Clearly, the exact nature of the relative orientation distributions in a real situation will depend on the experimental conditions (temperature, field type, field strength, polarisability, moment of inertia, etc) but, in general, shorter fibers will be less strongly oriented.…”

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

“…In figure 7, we plot this rescaled tumbling time as a function of the fibre length, all other parameters being kept constant. As can be observed, the longer 185 the fibre, the faster it tumbles, which differs from results obtained by Yamamoto and Matsuoka (1993) for rigid fibers in the viscous shear flow of a Newtonian fluid (in accordance with predictions by Jeffery (1922)) and by S lowicka et al (2012) for a single (but generally shorter) fibre in a Newtonian Poiseuille flow. However, let us first note that the tumbling time quickly reaches a steady value 190 τ 0 ≃ 20 when the fibre length exceeds 50 particles.…”

“…In a Newtonian fluid, the tumbling time should be equal to half the period predicted by Jeffery (1922) for rigid ellipsoids of aspect ratio r: τ J = π × (r + 1/r). Extrapolating the effective 235 aspect ratio r * of a cylindrical rods that behaves like an ellipsoidal rod of aspect ratio r (Bretherton, 1962;Yamamoto and Matsuoka, 1993), we find r * = 35 for a fibre of length N = 50, which corresponds to τ J = 110 ≫ τ 0 . Hence the actual tumbling time that we observe in our simulations is much shorter than predicted in a Newtonian fluid by Jeffery.…”

“…where c b is a dissipation constant and v i and v j are the respective bubble Following the seminal works of Yamamoto and Matsuoka (1993), we model the deformable fibre as a string of N disks of radius R f = 0.6R 0 . This model is particularly appropriate within the bubble model, since the dynamics of these fibre particles can be computed together with the dynamics of the bubbles.…”

Simulation of single fiber dynamics

“…Chain connectivity is maintained by constraints, producing equations that must be solved iteratively and simultaneously with the equations of motion. This method has been shown to reproduce certain dynamics of isolated fibers 11 , and has been employed to investigate the single fiber contribution to the suspension viscosity 12 , flowinduced fiber fracture of isolated fibers 13 , and fiber suspension behavior 14 .…”