Orientation and rotational diffusion of fibers in semidilute suspension
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The dynamics of fiber orientation is of great interest for efforts to predict the microstructure and material properties of a suspension flow system. In this research a fiber-level, hybrid simulation method, LBM‒EBF (coupled lattice‒Boltzmann method with the external boundary force method) is undertaken to advance the current understanding of the hydrodynamic interaction induced rotational diffusion mechanism for rigid fibers in semidilute suspension of low Reynolds number flow. The LBM‒EBF simulations correctly predict the orbit constant distribution of fibers in a sheared semidilute suspension flow. It is demonstrated that an anisotropic, weak rotary diffusion model can fit the orbit constant distribution very well, but it can not describe the asymmetry in Stokes flow observed in semidilute suspension. The rotational diffusion process is then characterized with a three dimensional spatial tensor representation of the rotational diffusivity. A scalar measure of the rotational diffusion‒'scalar Folgar‒Tucker constant', C[subscript I], is extracted from this tensor. The study provides substantial numerical evidence that the range of C[subscript I] (0.0038 to 0.0165) obtained by Folgar&Tucker (J. reinf. plast. and comp, v.3, 1984) in a semidilute regime is overly diffusive, and that the correct magnitude is of O(10⁻⁴). The study reveals that the interactions among fibers become more frequent with either the decrease of fiber aspect-ratio, r[subscript p] (keeping nL³ constant, where n is the fiber number density, and L is the fiber length) or with the increase of nL³ (keeping r[subscript p] constant) in the semidilute regime, which in consequence causes an increase in C[subscript I]. The rheological properties of sheared semidilute suspension are also computed with direct LBM‒EBF simulations. The LBM‒EBF investigation is extended to characterize the fiber orientation in a linearly contracting channel similar to a paper machine 'headbox'. It is found that the rotational diffusion is the predominant term over the strain rate in the semidilute regime for a low Reynolds number flow, and it results in a decreasing trend of rotational Peclet number, Pe, along the contraction centerline. Lastly, in order to improve the numerical consistency of the existing LBM‒EBF approach, a modification to the body force term in the LB equation is suggested, which can recover the exact macroscopic hydrodynamics from the mesoscale.