Critical Size of Continuum Theory Applicability for Single-Phase Liquid Flow in Nanochannel

As is well known that the continuum theory may fail to describe liquid flow in nanopores in geological systems due to size effect. However, the critical size for its applicability has never been clarified yet. This work presents such a clarification by comparing the continuum theory to molecular dynamic (MD) results of liquid flow in nanochannels. A simple simulation system is first considered with non-distinguishing molecular structures for channel wall and fluid for a general study. Subsequently a few typical mineral channels in real geophysical systems are modeled, with water or methane liquid flowing through them. The results indicate that the Navier-Stokes equation with non-slip boundary condition at the wall is applicable with acceptable error (less than 10% in comparison to MD results), as long as the channel height is larger than 100 molecular mean spacings. After boundary condition modification to account the liquid sticky layer or velocity slip adjacent to the wall, the Navier-Stokes equation remains still available for a channel height down to 10 molecular mean spacings. When the channel height is smaller than 10 molecular mean spacings, the continuum theory may totally break down for liquid flow in nanochannel.