A fractional-order approach for transient creeping flow of spheres

We provide experimental observations of power-law temporal response for spheres in the transient regime of a Stokes flow under the effect of gravity. The analysis of the fundamental physical mechanism leading to this unexpected behavior is performed via the fractional order solution of the Basset problem proposed in 1995 by Mainardi et al. [Proc. CANCAM 95(2), 836–837 (1995)]. In this study, the original solution was slightly modified via the introduction of non-dimensional parameters in order to account for the concurrent effects of inertial and viscous forces under the long transient regime. The solution correlates well with the obtained experimental results not only for small solid spheres (where the Stokes flow regime applies) but also for larger spheres. Results suggest that, during the transient response, memory effects may lead to the occurrence of a force (a generalized Basset force) that causes the observed anomalous diffusive dynamics and which is ultimately responsible for the discrepancy between experimental observations and classical Stokes solutions.