A New One-Equation Model of Fluid Drag for Irregularly Shaped Particles Valid Over a Wide Range of Reynolds Number

A new drag law for irregularly shaped particles is presented here. Particles are described by a
shape factor that takes into account both sphericity and circularity, which can be measured via the most
commonly used image particle analysis techniques. By means of the correlation of the drag coefficient versus
the particle Reynolds number and the shape factor, a new drag formula, which is valid over a wide range
of Reynolds number (0.03–10,000), is obtained. The new model is able to reproduce the drag coefficient of
particles measured in terminal velocity experiments with a smaller scatter compared to other laws commonly
used in multiphase flow engineering and volcanology. Furthermore, the new formula uses only one
equation, whereas previous models, to insure validity over an ample range, made use of a step function that
introduces a discontinuity at the switch of equations. Finally, this drag law works in the whole range of
variation, from extremely irregular particles to perfect sphere. A code of the iterative algorithm for the drag
coefficient calculation and terminal velocity is included in the supporting information both as a Fortran
routine and a Matlab function.