Hydrodynamic stability of helical growth at low Reynolds number

A cylindrical object growing at a low Reynolds number can spontaneously develop a helical shape. We have studied this phenomenon numerically, and our results may shed some light on the spontaneous formation of helical tails of a dense protein network observed in experiments on actin based motility. We also identify an unstable critical pitch angle which separates helices that straighten into rods from helices that flatten into planar curves as they grow. At the critical angle the pitch angle remains constant, whereas both helical diameter and pitch increase with the helical contour length.