Observations of fiber orientation in suspensions subjected to planar extensional flows

Fibers in a planar extensional flow tend to align parallel to the axis of extension, with a small orientational dispersion resulting from hydrodynamic, fiber–fiber interactions. We have visualized the orientation of an opaque, tracer fiber in the midst of an index of refraction and density matched fiber suspension in a four-roll mill and determined the mean squares of the components of the fiber orientation in the compressional and neutral directions. The observed mean-square orientations in suspensions in Newtonian fluids with nL3=5–17 are qualitatively consistent with the dilute limit of the theory of Shaqfeh and Koch Phys. Fluids A 31, 728 (1988). Here n is the number of fibers per unit volume and L is the fiber length. It was not possible to perform the experiment for higher fiber concentrations, because of difficulties in keeping the tracer fiber at the stagnation point, which were attributed to translational, hydrodynamic diffusion. Measurements of orientational dispersion in polyacrylamide solutions indicated that the non-Newtonian stresses increase fiber alignment, as predicted by Harlen and Koch Phys Fluids A 4, 5 (1992).