Near-wall Estimates of the Concentration and Orientation Distribution of Semi-dilute Rigid Fiber Suspensions in Poisieulle Flow

Abstract

A model is presented to describe the orientation and concentration state of semi-dilute, rigid fiber suspensions in a rectangular channel flow. A probability distribution function is used to describe the local orientation and concentration state of the suspension and evolves according to a Fokker-Plank type equation. Long range hydrodynamic fiber-fiber interactions are modeled using the approach outlined by Folgar and Tucker (J. Reinforced Plast. Comp. 3 98–119 1984). Near the channel walls, we apply the no-flux boundary conditions proposed by Schiek and Shaqfeh (J. Fluid Mech. 296, 271–324, 1995). Geometric constraints are used to couple the fibers’ rotary motion with its translational motion. This eliminates physically unrealistic orientation states in the near-wall region. A two-way coupling between the fiber orientation state and the momentum equations of the suspending fluid is considered. Experiments are performed to validate the numerical model by visualizing the motion of tracer fibers in an index-of-refraction matched suspension. The orientation distribution function is determined experimentally as a function of channel height. The results indicate that at distances less than one half fiber length from the channel walls, the model accurately predicts the available fiber orientation states and the distribution of fibers amongst these states. The model further predicts a sharp concentration gradient in this region.