Finite-size spherical particles in a square duct flow of an elastoviscoplastic fluid: an experimental study

The present experimental study addresses the flow of a Yield Stress Fluid (YSF) with some elasticity (Carbopol gel) in a square duct. The behaviour of two fluids with lower and higher yield stress is investigated in terms of the friction factor and flow velocities at multiple Reynolds numbers $Re^* \in$ (1, 200) and, hence, Bingham numbers $Bi \in$ (0.01, 0.35). Taking advantage of the symmetry planes in a square duct, we reconstruct the entire 3-component velocity field from 2-dimensional Particle Image Velocimetry (PIV). A secondary flow consisting of eight vortices is observed to recirculate the fluid from the core towards the wall-center and from the corners back to the core. The extent and intensity of these vortices grows with increasing $Re^*$ or, alternately, as the plug-size decreases. The second objective of this study is to explore the change in flow in the presence of particles. To this end, almost neutrally-buoyant finite-size spherical particles with duct height, $2H$, to particle diameter, $d_p$, ratio of 12 are used at two volume fractions $\phi$ = 5 and 10\%. Particle Tracking Velocimetry (PTV) is used to measure the velocity of these refractive-index-matched spheres in the clear Carbopol gel, and PIV to extract the fluid velocity. Additionally, simple shadowgraphy is also used for qualitatively visualising the development of the particle distribution along the streamwise direction. The particle distribution pattern changes from being concentrated at the four corners, at low flow rates, to being focussed along a diffused ring between the center and the corners, at high flow rates. The presence of particles induces streamwise and wall-normal velocity fluctuations in the fluid phase; however, the primary Reynolds shear stress is still very small compared to turbulent flows. The size of the plug in the particle-laden cases appears to be smaller than the corresponding single phase cases. Similar to Newtonian fluids, the friction factor increases due to the presence of particles, almost independently of the suspending fluid matrix. Interestingly, predictions based on an increased effective suspension viscosity agrees quite well with the experimental friction factor for the concentrations used in this study.