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 a two-fluid mixture constituted of water and ethanol inside carbon nanotubes at 20^{∘}C is considered. When diameters are small enough, nanotubes are filled with a 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, then the flow can be several hundred thousand times larger than Poiseuille flow.