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

Abstract

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 8 B 8 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 particleparticle 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.

Pair-particle trajectories in a shear flow of a Bingham fluid

“…However, as expected in the absence of inertia, fore-aft symmetry of particles trajectories is observed here in all cases. This last observation is in contradiction with experimental observations of fore-aft asymmetry in a paper under review at the same time as our paper [21] ; in yield stress fluids such as concentrated microgel suspensions, important elastic effects -absent in our simulations -may indeed lead to fore-aft asymmetry [22] .…”

“…The departure from this flow driven motion to a regime in which interparticle hydrodynamic interaction affects the particle trajectories depends on Bn : increasing the Bingham number seems to decrease the range of interparticle hydrodynamic interaction. This is consistent with the recent experimental observations of Firouznia et al [21] for particles trajectories in a Carbopol gel. It is reminded that the slight departure from symmetry in Fig.…”

“…15 and 16 even it is clearly seen that the flow is strongly modified in the area between the particles. A convenient quantitative evaluation of hydrodynamic interaction ranges has been proposed by [21] . As they did, we compute the normalized norm of the difference between the computed velocity field and the far field velocity (ie the quantity || − ̇ ‖|∕ max || ||) over the domain Ω\ P ( t ).…”

Computational modeling of multiphase viscoelastic and elastoviscoplastic flows

“…In most of these applications, we are dealing with multiphase flows. [1][2][3][4][5][6][7] Therefore, there is a compelling need to study multiphase flows of EVP fluids and predict their flow dynamics in various situations, including three-dimensional and inertial flows. The EVP materials exhibit simultaneously elastic, viscous, and plastic properties.…”

“…Biological and smart materials can be EVP, making the EVP fluid flows relevant for problems in physiology, biolocomotion, tissue engineering, and beyond. In most of these applications, we are dealing with multiphase flows . Therefore, there is a compelling need to study multiphase flows of EVP fluids and predict their flow dynamics in various situations, including three‐dimensional and inertial flows.…”