A new shape dependent drag correlation formula for non-spherical rough particles. Experiments and results

• A new shape-dependent particle-fluid drag law is presented.
• The law has been obtained from free-fall experiments of volcanic particles.
• The experiments cover a particle Reynolds number from 0.03 to 10,000.
• The model correctly predicts terminal velocities of rough non-spherical particles.
• The model is useful for environmental applications (e.g. volcanic ash slow settling).

The drag of non-spherical rough particles has been investigated in a wide range of Reynolds numbers (0.03–10,000). The study is based on experimental measurements of the terminal velocities of irregular particles falling in fluids of different densities and viscosities. The particle shape is described by a shape factor that takes into account both sphericity and circularity, which are measured via image particle analysis techniques. This shape factor is particularly suitable for non-spherical and highly irregular particles. The drag coefficient has been correlated to the particle Reynolds number and the shape factor and a new correlation law has been found; the correlation has the functional form of a power law. Due to the mutual dependency of the particle terminal velocity on the drag coefficient, which in turn depends on the particle shape and Reynolds number, an iterative procedure needs to be designed for calculating the terminal velocity of particles of a specific size and shape. Such a procedure is adopted herein and a spreadsheet and a Fortran 90 code allowing the iterative calculation are provided in the Supplementary Material. The fitting of experimental measurements with our model calculations show that our new law predicts the drag coefficients and the terminal velocity of irregularly shaped particles, as volcanic ash, more accurately than other shape-dependent drag laws.

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