Determination of Drag Coefficients in Measuring Particle Diameters

A systematic error exists in sedimentation techniques used for measuring particle diameters. This intrinsic shortcoming overestimates sizes of fine particles and underestimates coarse particles, and thus decreases the spread of particle sizes as estimated by sieving and other methods. This paper develops a method for estimating the contact area between a particle and the fluid, which is critical in calculating the nondimensional drag coefficient (CD). When a spherical particle falls in noncompressible, thermally homogeneous, and static fluid conditions, CD is a function of the Reynolds number and the contact area of the particle. Beyond the Stokes range, CD varies with the particle Reynolds number and the nature of the resistance. This theory is tested using glass spheres and natural eolian dune deposits falling in a still-air settling tube. Empirical equations for estimating CD values are developed. The measured aerodynamic-equivalent diameters of spherical particles equal their geometric diameters with a shape factor of unity. The aerodynamic-equivalent diameters of irregularly shaped particles are smaller than that of spherical particles for given geometric diameters of particles having the same mass, volume, and density. The findings have wide applications in sedimentary, environmental, and industrial analyses.