Dewetting, partial wetting and spreading of a two-dimensional monolayer on solid surface

We study the behavior of a semi-infinite monolayer, which is placed initially on a half of an infinite in both directions, ideal crystalline surface, and then evolves in time due to random motion of the monolayer particles. Particles dynamics is modeled as the Kawasaki particle-vacancy exchange process in the presence of long-range attractive particle-particle interactions. In terms of an analytically solvable mean-field-type approximation we calculate the mean displacement X(t) of the monolayer edge and discuss the conditions under which such a monolayer spreads (X(t) > 0), partially wets (X(t) = 0) or dewets from the solid surface (X(t) < 0).