Modeling the Drag Force of a Spherical Particle in Herschel–Bulkley Fluids

Particle-laden two-phase flows in viscous non-Newtonian fluids are ubiquitous in engineering applications, and their prediction requires accurate particle drag force models. In this work, we perform numerical simulations of the flow past a spherical particle in viscous non-Newtonian fluids, specifically Herschel–Bulkley fluids. Compared with previous studies, the present work extends the power-law index into the shear-thickening regime, covering a range from 0.2 to 1.8. Correspondingly, the simulations span particle Reynolds numbers from 5 to 200 and Bingham numbers from 0 to 10. Based on the simulation data, symbolic regression is employed to derive an explicit correlation for the drag coefficient of the spherical particle as a function of the three dimensionless parameters: the particle Reynolds number, Bingham number, and power-law index. These specific ranges clearly define the applicability of the proposed model. The resulting correlation provides an accurate predictive model for practical predictions of particle-laden two-phase flows of Herschel–Bulkley fluids.