Fading “memory” and “anomalies” in fluid flows - The Basset force as an example

Abstract: The drag on a solid sphere immersed in an incompressible fluid has been a topic of research for over almost 200 years. The drag on a sphere accelerating in a quiescent fluid commonly contains a contribution from steady viscous drag, added mass due to accelerating the fluid, and the so-called Basset “history”, viscosity dependent term. Some disagreement of the importance of the Basset term is evident in the literature. The Basset term was found to decay as t^-1/2, t^-2 or even exponentially, depending on conditions on particle acceleration/motion or the ambient flow. Unexpected behavior of the flow (termed here as anomalies) may occur. The origin and the remedy to anomalies due to assumption related to derivations of the expression of the drag on a single sphere are discussed.