Predicting wall drag coefficient and settling velocity of particle in parallel plates filled with Newtonian fluids

Abstract The hindrance of boundary to particle transport exists widely in various industrial applications. In this study, the wall drag force of parallel plates on settling particles was revealed through settling experiment. High-speed camera was used to record and analyse the settling process of particles in parallel plates that are filled with Newtonian fluids. A total of 600 experiments were carried out, involving the range of relative diameter and particle Reynolds number of 0.01–0.95 and 0.004–14.30, respectively. The wall drag coefficient was defined to quantitatively analyse the wall drag force of the parallel plates. The influence of relative diameter, particle properties, rheological properties, and the settling dynamic process on the wall drag coefficient was revealed, and the wall drag coefficient model with mean relative error of 5.90% was established. Furthermore, an explicit settling velocity model with mean relative error of 8.96% for the particle in parallel plates was developed by introducing a dimensionless variable independent of settling velocity, the Archimedes number. Finally, a calculation example was provided to clarify the using process of the explicit model. This research is expected to provide guidance for optimizing water hydraulic fracturing in the oil and gas industry.