Model for spreading of liquid monolayers.

Manipulating fluids at the nanoscale within networks of channels or chemical lanes is a crucial challenge in developing small scale devices to be used in microreactors or chemical sensors. In this context, ultrathin (i.e., monolayer) films, experimentally observed in spreading of nanodroplets or upon extraction from reservoirs in capillary rise geometries, represent an extreme limit which is of physical and technological relevance since the dynamics is governed solely by capillary forces. In this work we use kinetic Monte Carlo (KMC) simulations to analyze in detail a simple, but realistic model proposed by Phys. Rev. Lett. 76, 86 (1996)]] for the two-dimensional spreading on homogeneous substrates of a fluid monolayer which is extracted from a reservoir. Our simulations confirm the previously predicted time dependence of the spreading, X ( t--> infinity ) =A square root of t, with X (t) as the average position of the advancing edge at time t, and they reveal a nontrivial dependence of the prefactor A on the strength U0 of interparticle attraction and on the fluid density C0 at the reservoir as well as an U0 -dependent spatial structure of the density profile of the monolayer. The asymptotic density profile at long time and large spatial scale is carefully analyzed within the continuum limit. We show that including the effect of correlations in an effective manner into the standard mean-field description leads to predictions both for the value of the threshold interaction above which phase segregation occurs and for the density profiles in excellent agreement with KMC simulation results.