The buckling, folding, and coiling of thin sheets and
filaments of solids and fluids take place on length
scales spanning several orders of magnitude, in phenomena ranging from orogenesis in geophysics to materials
processing and soft-matter physics. For example, when an
elastic rope is fed uniformly toward a horizontal plane, it first
buckles and eventually coils into a spool that is deposited
onto the plane.1 A similar phenomenon also occurs when a
slender viscous fluid jet impinges onto a horizontal plane and
leads to the deposition of a liquid rope coil.2 In either case,
although the scale of the coil and the speed of coiling are
determined by the balance between the internal elastic or
viscous forces that resist deformation and a combination of
inertia and gravity, the basic phenomenology is a consequence of geometry which favors bending deformations
over stretching modes.
Here, we consider the spon