  Motivated by the intriguing motility of spirochetes (helically-shaped
bacteria that screw through viscous fluids due to the action of internal
periplasmic flagella), we examine the fundamental fluid dynamics of
superhelices translating and rotating in a Stokes fluid. A superhelical
structure may be thought of as a helix whose axial centerline is not straight,
but also a helix. We examine the particular case where these two superimposed
helices have different handedness, and employ a combination of experimental,
analytic, and computational methods to determine the rotational velocity of
superhelical bodies being towed through a very viscous fluid. We find that the
direction and rate of the rotation of the body is a result of competition
between the two superimposed helices; for small axial helix amplitude, the body
dynamics is controlled by the short-pitched helix, while there is a cross-over
at larger amplitude to control by the axial helix. We find far better, and
excellent, agreement of our experimental results with numerical computations
based upon the method of Regularized Stokeslets than upon the predictions of
classical resistive force theory.
