The analytic solution of Stokes for time-dependent creeping flow around a sphere: Application to linear viscoelasticity as an ingredient for the generalized Stokes–Einstein relation and microrheology analysis

Analytic expressions for the transient stream function, transient flow field, and transient pressure field for creeping flow around a sphere are derived. An analytic expression for the total force on the sphere is also found. The approach is essentially that of Stokes from 1856. Aside from the (essentially trivial) generalization to linear viscoelastic fluids, there is nothing novel in the derivation. Our purpose is to (1) point out that Stokes, not Basset or Boussinesq derived it first, (2) show how simple the derivation is, which may be compared to the more famous solution of Landau and Lifshitz, (3) show an application of the correspondence between creeping flow and linear viscoelastic flow solutions, and (4) provide sufficiently detailed notes so that the derivation might be given in a graduate fluid dynamics or transport phenomena lecture.

► Stokes, not Basset or Boussinesq first derived the time-dependent creeping flow around a sphere.
► Stream functions make the problem very straightforward, as the detailed derivation shows.
► The result is trivially generalized to linear viscoelastic media.
► The derivation makes a suitable example in a graduate fluids or rheology course