There are many types of almost frictionless and very rapid flows of complex molecules in nature. One example is the almost frictionless nature of the protein channel aquaporin-1. Nearly frictionless transport of complex biomolecular fluids along a membrane composed of wavy-rough nanoannuli was investigated by using the verified Eyring’s transition-state approach (cf. Journal of Physical Chemistry B, Vol. 112, 2008, pp. 3019-3023.), together with a boundary perturbation approach, which has been successfully adopted to study the selective transport of polymeric matter in confined nanodomains. The critical parameters related to the rapid or nearly frictionless transport of biomolecules were identified to be directly relevant to the possible phase-transition temperature after selecting specific activation energies and activation volumes for fixed confined (cylindrical) geometry as well as small wavy corrugations along the interface. Our results can also make the membrane composed of aligned wavy-rough nanotubes a promising mimic of protein channels for transdermal drug delivery and selective chemical sensing.