Time-dependent effects in high viscosity fluid dynamics

Flows dominated by high viscosity are often described using the steady Stokes equation. We will discuss three situations where the limits that are needed in order to arrive at this representation are questionable, and will show that unexpected flow behaviour arises: (i) under the influence of a time-dependent force, flows need not be reversible and chaotic advection can arise; (ii) the flow field around an oscillating sphere becomes that of the steady flow only for slow motion and sufficiently close to the sphere; (iii) the time-dependence in the fluid motion modifies the response of a sphere to an oscillatory force; (iv) when these forces are taken into account, the limits of particle size to zero and observation time to infinity do not commute and small particles do not maintain a uniform distribution.