Settling dynamics of two identical vertically aligned spheres in a thixotropic fluid

Despite the great relevance of particle dynamics in non-Newtonian fluids, particles settling in non-Newtonian fluids has received limited scientific attention. The simple case of two vertically aligned spheres settling in a thixotropic xanthan fluid is considered using solutions of xanthan + glycerol + water and 0.75 mm radius stainless steel spheres. Chaining phenomenon is observed where the trailing sphere velocity is increased due to a corridor of reduced viscosity created by the leading sphere. Our experimental methods are first validated against a Newtonian fluid of glycerol + water in which the sphere velocities remained equal. Using the fluid velocity induced by a single sphere, the two sphere velocities are approximated by Faxén's first law. In a non-Newtonian (thixotropic) xanthan fluid, a viscosity ratio is introduced to account for the reduced fluid viscosity encountered by the trailing sphere due to the slow structure recovery of the fluid after shear thinning. The viscosity ratio is an exponential decay function dependent on the time between spheres normalised by the fluid recovery time, a parameter which is experimentally determined. When the sphere-sphere separation is large, the viscosity ratio tends towards unity. The predicted settling velocities show good agreement with experimental data.