We propose a new Eulerian model for the internal transport of mass, momentum, and energy during convective drying of a two-phase deformable medium (solid–binary liquid). The description at the phase scale is made through the classic equations of continuum mechanics, which are then homogenized by the volume-averaging method. The classical conjecture on the relation between the liquid pressure and the liquid volume fraction is unnecessary. Simulations show that the main mechanism for water migration is the advection produced by the liquid pressure gradient superimposed to the velocity of the solid phase.