The stress-driven diffusion of solute atoms to a slowly moving brittle crack is studied under the condition of pure drift. The first-order drift-diffusion equation for a slowly moving crack at uniform velocity is solved yielding the flow lines and the impurity segregation rate in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the solute migration kinetics near a steadily advancing subcritical crack at stage I and stage II crack growth.