Navier number and transition to turbulence

The motivation behind this article is to explain a role of the Navier number (Na - dimensionless slip-length) in prediction of closures for laminar to turbulent transition undergoing via eddies detachment from the slip layer in nano-cannals. Additionally the role of the Navier number Na in universal modeling of phenomenon of enhanced mass flow rate reported in micro-and nano-channels has been explained. The Na number should be treated as a ratio of internal viscous to external viscous momentum transport and therefore this notion cannot be extended onto whole friction resistance phenomena. Our proposal for unique expressing of a critical point in turbulence transition is that on a plane of f(D) - Re one needs two coordinates. The second critical coordinate has been discovered by Stanton and Pannell and is known to be the Stanton-Pannell number StPa. Finally dependence of the Stanton-Pannell number StPa on Navier number Na and Reynolds number Re is presented.