The main purpose of this work is to show that the gravity term of the segregation-mixing equation of fine mono-disperse particles in a fluid can be derived from first-principles (i.e., elementary physics). Our derivation of the gravity-driven flux of particles leads to the simplest case of the Richardson and Zaki correlation. Stokes velocity also naturally appears from the physical parameters of the particles and fluid by means of derivation only. This derivation from first-principle physics has never been presented before. It is applicable in small concentrations of fine particles.