The fluid flow and solute segregation which occur during directional solidification, including effects of gravity and microgravity were studied. The nature of the fluid flow, its effects on the shape of the crystal-metal interface and the resulting distribution of solutes are examined. During solidification of a binary alloy at constant velocity vertically upwards, thermosolutal convection occurs if the solute rejection or preferential incorporation at the crystal-melt interface decreases the density of the melt. Numerical calculations of the solute, temperature, and flow fields are carried out by using previously developed algorithms for Schmidt numbers Sc = 1, 10, 81. The time periodic flow, which occurs over a narrow range of parameters, is investigated.