Stokes flow through a coiled tube

Stokes flow through a coiled tube with arbitrary cross-section is investigated by perturbation expansions in the limit where the helical pitch is either small or large compared to the radius of the helical centerline. The problem is formulated using two alternative non-orthogonal helical coordinate systems applicable to these two opposing limits. The solutions of the respective zeroth-, first-, and second-order perturbation problems are computed by finite element methods for unidirectional, axisymmetric, and two-dimensional Stokes flow. Computations are carried out for tubes with circular and square cross-sections oriented in different ways. The results illustrate the effect of the tube geometry on the hydraulic conductivity and kinematic structure of the flow.