Application of constitutive equation considering fiber orientation in shear flow of fiber suspension

This study focuses on the parameters of the constitutive equation proposed by Lipscomb et al. and the fiber orientation behavior predicted by the F-T-S model which is added a slip factor to Folgar-Tucker isotropic rotary diffusion (IRD) model. For comparing numerical and experimental data, the step shear experiments are conducted to fiber suspension. The fiber orientation was visualized by a microscope attached to a rotational rheometer. The visualization can observe the azimuth angle of fibers, but it lacks the polar angle. Hence, we converted the orientation tensor to a spatial two-dimensional orientation tensor, i.e. the polar angle is eliminated. The model prediction fitted to the experimental data to determine the parameter values. Then, the values were compared with some equations suggested by the other researchers. It is found that the predicted orientation tensor is almost matched to experimental ones, but the mismatch on shear viscosity is enlarged with the increasing fiber volume fraction of suspensions. The model parameter values depend on the material coefficient as the fiber volume fraction. One parameter (interaction parameter of the F-T-S model is agreed with the equation by Phan-Thien et al. However, the other parameters disagreed with some equations.