  The aim of the paper is the study of fluid mixtures in nanotubes by the
methods of continuum mechanics. The model starts from a statistical
distribution in mean-field molecular theory and uses a density expansion of
Taylor series. We get a continuous expression of the volume free energy with
density's spatial-derivatives limited at the second order. The nanotubes can be
filled with liquid or vapor according to the chemical characteristics of the
walls and of liquid or vapor mixture-bulks. An example of two-fluid mixture
constituted of water and ethanol inside carbon nanotubes at 20{\textdegree} C
is considered. When diameters are small enough, nanotubes are filled with
liquid-mixture whatever are the liquid or vapor mixture-bulks. The carbon wall
influences the ratio of the fluid components in favor of ethanol. The
fluid-mixture flows across nanotubes can be much more important than classical
ones and if the external bulk is vapor, the flow can be several hundred
thousand times larger than Poiseuille flow.
