The long wavelength limit of a recent microscopic phase field crystal (PFC)
theory of a binary alloy mix- ture is used to derive an analytical
approximation for the segregation coefficient as a function of the interface
velocity, and relate it to the two-point correlation function of the liquid and
the thermodynamic properties of solid and liquid phases. Our results offer the
first analytic derivation of solute segregation and solute drag de- rived from
a microscopic model, and analytically support recent molecular dynamics and
fully numerical PFC simulations. Our analytical result also provides an
independent framework, motivated from classical density functional theory, from
which to elucidate the fundamental nature of solute drag, which is still highly
contested in the literature.