Sedimentation of spheroids in Newtonian fluids with spatially varying viscosity*

This paper examines the rigid body motion of a spheroid sedimenting in a Newtonian fluid with a specified, spatially-varying viscosity field.  We leverage the arguments of symmetry to find the general expression for the particle’s mobility tensor relating the external force and torque with the spheroid's velocity and rotation rate. We find that a constant viscosity gradient does not alter force/velocity and torque/rotation couplings; however, the force/rotation and torque/velocity couplings are altered. Illustrative examples obtained via reciprocal theorem based estimation of the mobility tensor show that the sedimenting spheroid exhibits a multitude of different behaviors ranging from  tumbling to stable orientations, based on the shape of the particle(aspect ratio) and the direction of the viscosity gradient. These results are markedly different from the case when the fluid has spatially uniform viscosity and the spheroid sediments with a constant initial orientation.

This work was supported by the American Chemical Society Petroleum Research Fund under grant ACS PRF 61266-DNI9.