We have studied the phase separation of a system with a conserved orde
r parameter in the presence of a flat surface via Monte Carlo simulati
ons. For various quench parameters, we observed the domain growth in a
surface layer. The kinetics of this ordering was studied, both in the
presence and absence of bulk phase separation. In the absence of bulk
phase separation, the surface domains were found to follow model A gr
owth kinetics. In the presence of bulk phase separation. a crossover i
n the surface kinetics between model A and model B dynamics was observ
ed.