GROWTH OF A SINGLE DROP FORMED BY DIFFUSION AND ADSORPTION OF MONOMERS ON A 2-DIMENSIONAL SUBSTRATE

We study a single, motionless three-dimensional (3D) drop growing by a dsorption of diffusing monomers on a 2D substrate. A simple treatment based on a quasistatic approximation predicts that the radius of the d rop increases as [t/ln(t)]1/3 in the long-time limit. By applying the method of matched asymptotic expansions we then confirm that the quasi static approximation provides a dominant asymptotic behavior. We also show that the typical distance from the surface of the growing drop to the nearest surviving monomer scales as [ln(t)]1/2 and discuss the di stribution function for that minimum distance.