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This paper examines the rigid body motion of a spheroid sedimenting in aNewtonian fluid with a spatially varying viscosity field. The fluid is at zeroReynolds number, and the viscosity varies linearly in space in an arbitrarydirection with respect to the external force. First, we obtain the correctionto the spheroid's rigid body motion in the limit of small viscosity gradients,using a perturbation expansion combined with the reciprocal theorem. Next, wedetermine the general form of the particle's mobility tensor relating its rigidbody motion to an external force and torque. The viscosity gradient does notalter the force/translation and torque/rotation relationships, but introducesnew force/rotation and torque/translation couplings that are determined for awide range of particle aspect ratios. Finally, we discuss results for thespheroid's rotation and center-of-mass trajectory during sedimentation.Depending on the viscosity gradient direction and particle shape, a steadyorientation may arise at long times or the particle may tumble continuously.These results are significantly different from the case when no viscositygradient is present, where the particle stays at its initial orientation forall times. The particle's center of mass trajectory can also be altereddepending on the particle's orientation behavior, for example giving rise todiagonal motion or zig-zagging motion. We summarize the observations forprolate and oblate spheroids for different viscosity gradient directions andprovide phase plots delineating different dynamical regimes. We also provideguidelines to extend the analysis when the viscosity gradient exhibits a morecomplicated spatial behavior.

Sedimentation of spheroids in Newtonian fluids with spatially varying viscosity