The motion of ellipsoids in a second order fluid

The rigid body motion of an ellipsoid in a second order fluid (SOF) under the action of specified (time independent) external forces and torques have been obtained to first order in the Weissenberg number by inverting the resistance relations for the force an torque under specified rigid body motions. The reciprocal theorem of Lorentz was used to bypass the calculation of the O(W) velocity field. The results agree with known analytic solutions for SOF with the secondary to primary normal stress ratio of -1/2. The solution procedure was also tested by computing the torque on a translating prolate spheroid with aspect ratios ranging from slender bodies to near-spheres. One result is that for a SOF with zero secondary normal stress (Weissenberg fluid), previous asymptotic results for near-spheres were found to be accurate even at fairly large aspect ratios. New results of nondegenerate ellipsoids suggest that the orientation (as monitored by Euler angles) and trajectory of sedimenting, nonaxisymmetric particles such as ellipsoids provide useful information on the rheology of the suspending fluid.