Dynamic simulation of fiber suspensions in shear flow

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Abstract
A new method is presented to simulate the motion of concentrated fiber suspensions in shear flow at low Reynolds numbers without Brownian motion. The hydrodynamic interaction among fibers is considered in a particle simulation method (PSM), in which a fiber is modeled by arrays of spheres. The motion of each constituent sphere of a fiber, which are dispersed into a unit cell with periodic boundaries, is followed to predict the microstructure and the rheological properties. The hydrodynamic interaction is decomposed into two parts, intra- and interfiber ones. In the former, the many-body problem is solved by calculating the mobility matrix for each fiber to obtain the hydrodynamic force and torque exerted on each sphere. In the latter, only the near-field lubrication force is considered between spheres of one fiber and another. The validity of this approximate treatment was first examined for the sphere dispersed system. The simulated microstructure and the rheological properties were in very good agreement with results of both experiments and the Stokesian dynamics. The methodology was then applied to concentrated rigid and flexible fiber suspensions. The overshoot of suspension viscosity was observed at the early stage for rigid fiber suspensions, but not for flexible ones. This was because of the transient change of the microstructure from the flow-directional orientation to the planar orientation of rigid fibers. The normal stress was calculated for the flexible fiber suspension and clearly showed that the elasticity of fiber suspensions was due to the deformation of fibers. The proposed simulation method can predict the effect of such parameters as the aspect ratio, flexibility, and volume fraction of fibers on the microstructure and the rheological properties of fiber suspensions.

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