The interaction of two spherical particles in simple-shear flows of yield stress fluids

This study focuses on the interaction of two small freely-moving spheres in a linear flow field of yield stress fluids. We perform a series of experiments over a range of shear rates and different shear histories using an original apparatus and with the aid of conventional rheometry, Particle Image Velocimetry (PIV) and Particle Tracking Velocimetry (PTV). We investigate the flow field around a single sphere as well as two spheres in a simple-shear flow. The flow is Stokesian and the Bingham number is in the range of 0 ≤ B ≤ 2. To explore the limit of zero Bingham number, we use both Newtonian and shear thinning suspending fluids. We use guar gum solutions and Carbopol gels as shear thinning and yield stress test fluids, respectively. We show that the presence of a slight elasticity, which is unavoidable when dealing with polymer solutions, plays an important role in establishing the flow field, e.g., disturbance velocities and stream lines around a single sphere as well as particle trajectories. Therefore, ideal yield stress fluid models cannot provide a full description of flow problems involving particles in practical yield stress fluids. The flow field around a single sphere can be used to understand the two particle interactions. We show how particle-particle contact and non-Newtonian behaviors result in relative trajectories with fore-aft asymmetry. Particularly, the fore-aft asymmetry depends on the Deborah number, Bingham number, shear history, initial offset and roughness of the particles. Finally, we discuss how the relative particle trajectories may affect the microstructure of complex suspensions and consequently the bulk rheology.