Superfluid Behavior of Start-Up Flows in Nano-Channels
Vladimir V. Kulish and Weng-Kong Chan
The paper presents the equation of fluid flow, derived from the assumption that there is a finite time lag between the onset of the shear stress and the corresponding velocity gradient. An integral solution of a truncated version of the one-dimensional version of the equation is obtained. Then, the start-up Couette flow in a flat nano-channel is investigated to illustrate the model’s applicability. It is shown that start-up flows exhibit superfluid behavior, which becomes fully pronounced when the characteristic size of the channel becomes of the order of nanometers. The conclusion is drawn that superfluidity is the manifestation of the wave energy transport, in the case when the diffusion transport is small or negligible in comparison.