Summary of frictional drag coefficient relationships for spheres: Evolving solution strategies applied to an old problem

In 1851 Stokes reported his analytical solution for the kinetic force (form drag plus frictional drag) exerted by an unbounded fluid on a steadily falling sphere under very slow or creeping flow conditions. This so called Stokes' law was improved in the early 20th Century by several authors, who included diverse approximations to the inertia term neglected by Stokes in the Navier-Stokes equation describing Newtonian fluid motion around the sphere. Lapple and Shepherd (1940) followed this fundamental theoretical work with a landmark plot relating the experimental frictional drag coefficient f (directly proportional to the magnitude of the kinetic force) to the sphere diameter-based Reynolds number (Re) for 0.1 <= Re <= 3.0E+06. Researchers quickly realized that Stokes' law (valid for Re < 0.1) was insufficient to explain the data over the entire span of Re, giving rise to new solution methodologies to predict f(Re). This communication gives a chronological listing of well-known f(Re) relationships, providing insights on the rationale and strategies used in their development. The modern chemical engineer can therefore readily assess the evolution of this problem and realize the remaining research gaps in the field of fluid flow around submerged spheres. (C) 2017 Elsevier Ltd. All rights reserved.