Reconstruction of the internal volume fraction for particle-liquid system from imaging indicators by refractive index matching

Refractive index matching (RIM) is widely used to investigate particle-liquid mixture flows. However, determining the volume fraction φ in RIM is generally empirical and lacks theoretical or experimental basis. To reasonably reconstruct the internal φ, this study performs systematic calibration experiments to study the relationship between φ and the imaging indicators. The results show that the model based on area fraction c_2D will induce a large error for low φ owing to the instability of the particle’s apparent size. The traditionally adopted proportional function φ = ac_2D is only valid for φ near the calibration point. A predictive model is proposed based on the size of the Voronoi cell, d_poly, which proves to be more accurate and stable in RIM experiments. The d_poly-based model is applied to dense granular flows down an inclined plane to study the internal profiles of φ and the bottom normal stress.