text: As the no-slip condition was an empirical observation, there are physical scenarios in which it fails. For sufficiently rarefied flows, including flows of high altitude atmospheric gases  and for microscale flows, the no-slip condition is inaccurate. For such examples, this change is driven by an increasing Knudsen number, which implies increasing rarefaction, and gradual failure of the continuum approximation. The first-order expression, which is often used to model fluid slip, is expressed as
  where  is the coordinate normal to the wall,  is the mean free path and  is some constant known as the slip coefficient, which is approximately of order 1. Alternatively, one may introduce  as the slip length. Some highly hydrophobic surfaces, such as carbon nanotubes with added radicals, have also been observed to have a nonzero but nanoscale slip length. 
   Similarly, some researchers have investigated this slip condition, modelling the cause as due to the high smoothness of highly-ordered nanoscale surfaces.
  While the no-slip condition is used almost universally in modeling of viscous flows, it is sometimes neglected in favor of the no-penetration condition (where the fluid velocity normal to the wall is set to the wall velocity in this direction, but the fluid velocity parallel to the wall is unrestricted) in elementary analyses of inviscid flow, where the effect of boundary layers is neglected.
  The no-slip condition poses a problem in viscous flow theory at contact lines: places where an interface between two fluids meets a solid boundary. Here, the no-slip boundary condition implies that the position of the contact line does not move, which is not observed in reality. Analysis of a moving contact line with the no slip condition results in infinite stresses that can't be integrated over. The rate of movement of the contact line is believed to be dependent on the angle the contact line makes with the solid boundary, but the mechanism behind this is not yet fully understood.