The "hydrodynamic position" of the wall `Z_H` is defined as the position at which the boundary condition on the macroscopic velocity field has to be applied.

`(frac{partial v_{x,y}(mathbf{r},t)}{partial z})_{z=Z_H}=frac{1}{L_s}v_{x,y}(mathbf{r},t)|_{z=Z_H}`

where `v_{x,y}` is the slip velocity, `L_s` is the slip length. The hydrodynamic position `Z_H` fluctuates as it is defined by the molecular trajectories as a result of collision with the wall.

Fluid in the dense state undergo frequent collisions with the wall as compared to a rarefied state. As a result the fluctuating "hydrodynamic wall" observed in a small time interval is density dependent for a given fluid-wall interaction.

Click on the images to view how hydrodynamic wall looks for rarefied and dense cases.