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# Hydrodynamic Wall

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.

Rarefied case

• Dense case