(328f) Sedimentation of Spheroids in Inelastic Fluids with Variable Viscosity

Fluids with inhomogeneous viscosity fields are ubiquitous. For example, certain biological fluids like mucus and extracellular microbial polymers are mixtures of fluids of different viscosities, and therefore exhibit variable viscosity, either with or without sharp viscosity gradients. Similarly, the gradients of temperature, salinity, concentration, may induce spatial variation in the viscosity, most commonly observed in marine ecosystems. Finally, suspensions of particles in Newtonian fluids, with otherwise constant viscosity, may be treated at the continuum level as fluids with viscosity varying with local volume fraction.

To understand the microhydrodynamics of particles in viscosity-stratified fluids, we study an idealized problem of a spheroid sedimenting in a zero Reynolds number fluid with an imposed viscosity gradient. We perform a perturbation expansion in the limit of weak viscosity gradients and determine the leading order correction to the spheroid’s rigid body motion. Under no viscosity gradient, we find that the spheroid stays in its initial orientation – a classical result arising from the symmetry of the Stokes equations. However, when a viscosity gradient exists, the particle takes on a preferred orientation depending on its shape and the direction of the imposed gradient. We map out the preferred orientation for a wide range of particle shapes and viscosity gradient directions. We also come up with a reduced-order theory, based on symmetry conditions, to obtain the full resistance matrices for the particle dynamics (i.e., the force-rotation and torque-translation coupling). This allows one to determine the spheroid’s dynamics under a wider range of problems where viscosity gradients exist.