Flow-Induced Alignment of Fibers in the Absence of Fiber-Fiber Interactions

Flow-induced alignment of non-spherical particles provides a practical and inexpensive means to control the microstructure of composite materials. Model predictions of the low-order statistical properties characteristic of the microstructure are often based on the moment equation for the orientation dyadic. The solution of this moment equation requires knowledge of both the fluid flow field (via the strain rate and vorticity dyadics) and the fiber orientation tetradic operator. Additional model parameters for the moment equation include the fiber-fluid coupling coefficient, which equals -1 for platelets and +1 for large aspect ratio fibers, as well as the phenomenological rotary diffusion coefficient, which accounts for fiber-fiber interactions. The solution to the moment equation for the orientation dyadic has been limited in the past by the absence of a practical closure model for the fiber orientation tetradic. Recently, Petty et al. (1999) identified a class of closure approximations that retain the six-fold symmetry and the six-fold projection properties of the exact fiber orientation tetradic operator associated with fiber-fluid interactions. Parks et al. (1999) used the new closure approximation and examined the behavior of the orientation moment equation for concentrated and dilute suspensions subjected to simple shear flows. The new closure approximation is used here to examine the transient response of the orientation dyadic for a class of simple flows in the absence of fiber-fiber interactions. Calculations are presented for fiber-fluid interaction coefficients ranging from -1 to +1.