Numerical analysis of the motion of a single fiber interacting with a solid wall in a wall-bounded shear flow

Abstract

In order to investigate the effect of a solid wall on the interaction between the motion of a fiber and a suspending fluid flow, direct numerical simulations of single-fiber dynamics in a wall-bounded shear flow are conducted. A Cartesian grid method using a consistent direct discretization approach and its extension to a moving boundary problem is used for accurate prediction of a three-dimensional fluid flow around a rotating fiber. The fiber is modeled as an ellipsoid with an aspect ratio ranging from 2 to 8, while the suspending fluid is assumed to be an incompressible Newtonian fluid with a particle Reynolds number of less than 0.1. After the validity of the simulations is ascertained in a far-field condition through comparisons with theoretical results, the wall effect on the fiber motion is investigated in detail. The wall effect appears when the minimum distance between the fiber and the wall c is less than 5 times the length of the major radius of the fiber b. The rotation period increases with decreasing fiber-wall distance and increasing aspect ratio, and the ratio of the rotation period with respect to the theoretical period is well normalized by (c/b)/(b/d), where d is the equivalent radius obtained from the cross-sectional area of the fiber. Based on visualization of the flow field, the fiber motion is found to be strongly affected by the hydrodynamic torque caused by the shear stress and the pressure distribution on the fiber surface. The pressure distribution acts as a decelerating torque on the fiber when the fiber is parallel to the wall, while it acts as an accelerating torque when the fiber is perpendicular to the wall. These pressure variations are augmented as the fiber-wall distance decreases, resulting in an increase in the rotation period as well as time-averaged fiber orientation in the streamwise direction.