Orientation tensors in simple flows of dilute suspensions of non-Brownian rigid ellipsoids, comparison of analytical and approximate solutions

Abstract

General analytical solutions are obtained for the planar orientation structure of rigid ellipsoid of revolutions subjected to an arbitrary homogeneous flow in a Newtonian fluid. Both finite and infinite aspect ratio particles are considered. The orientation structure is described in terms of two-dimensional, time-dependent tensors that are commonly employed in constitutive equations for anisotropic fluids such as fiber suspensions. The effect of particle aspect ratio on the evolution of orientation structure is studied in simple shear and planar elongational flows. With the availability of analytical solutions, accuracies of quadratic closure approximations used for nonhomogeneous flows are analyzed, avoiding numerical integration of orientation distribution function. In general, fourth-order orientation evolution equations with sixth-order quadratic closure approximations yield more accurate representations compared to the commonly used second-order evolution equations with fourth-order quadratic closure approximations. However, quadratic closure approximations of any order are found to give correct maximum orientation angle (i.e., preferred direction) results for all particle aspect ratios and flow cases.