An experimental investigation of settling velocity of natural sands in water using Particle Image Shadowgraph

• PIS technique to determine shape, size, and settling velocity of sand in water
• Practical approach correlating sieve diameter to equivalent diameter
• New correlations for predicting particle settling velocity of sand in water
• Predict particle settling velocity with 7.7% error for sieve size 0.19–1.22 mm
• Model is even more effective, with a 4.1% error, for particle size 0.35–1.18 mm

Considering the extensive industrial usage of sands and the benefits of improving the effectiveness of such applications, a detailed experimental study on settling of quartz sands in water is conducted. In this study, 980 quartz sand particles under four sieve sizes in the range of 0.35 mm–1.18 mm are used. Particle Image Shadowgraph (PIS), an accurate and efficient technique, is employed to determine the settling velocity of the particles. Using PIS in this novel application, the particle dimensions are characterized in terms of centricity, major/minor axes, and equivalent circular diameter. Using the shadowgraph results, an empirical model for settling velocity is developed based on a dimensionless diameter and Reynolds number. The dimensionless diameter is calculated from the equivalent circular diameter (Dc) for the actual projected area of the particle. Furthermore, a simplistic empirical model based on equivalent circular radius (Rce) is proposed in which the particles are considered to be elliptical. Both models require only two-dimensional size parameters that can be easily measured. In this work, drag coefficient (Cd) versus Reynolds number curve for sand particles in the intermediate regime is also presented. It is observed that Cd attains an approximate value of 0.95 at Rep > 160. Also, for particles within a particular sieve diameter range, a large variance (16.35% to 92.35%) in settling velocity is observed. Based on the experimental measurement, a correlation between mean sieve diameter and equivalent circular diameter (Dc) is developed which assists in more accurately predicting settling velocity. The new empirical models when compared with data in the literature predict the settling velocity with an average absolute error of 4.1% and 6.5%, respectively, for sieve sizes of 0.35 mm–1.18 mm.

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