Spreading of Liquid Monolayers on Homogeneous and Chemically Patterned Substrates - Kinetic Monte Carlo Simulations and Continuum Limit
Dr. Mihail N. Popescu (MPI für Metallforschung, Stuttgart)

Manipulating fluids at 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, ultra-thin (i.e., monolayer) films, experimentally observed in spreading of nano-droplets 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.

Using kinetic Monte Carlo simulations, we have confirmed [1] that a simple lattice gas model with interacting particles proposed in Ref. [2] indeed captures the experimentally observed time dependence of spreading for a liquid monolayer on a homogeneous substrate.
We show that the model predicts qualitatively different structures for the (experimentally measurable) density profiles along the spreading direction above and below of a critical value for the ratio between the fluid-fluid interaction and thermal energy. We analyze these profiles using a non-linear, uphill diffusion equation derived from the microscopic dynamics in the continuum limit.

In the case of patterned substrates, we have studied the transport of such liquid monolayers extracted form reservoirs in contact with a chemically heterogeneous flat surface on which domains of different wettability have been "imprinted" by assuming that the difference in wettability may be modeled solely by different chemical potentials.
Very simple patterns consisting of stripes with different wettability oriented along or perpendicular to the direction of flow have been considered. Our simulations indicate that it is possible to achieve lateral confinement of flow at relatively low chemical potential differences and that, surprisingly, in the case of the confined flow along a wettable stripe the mass transport is faster along the edges of the stripe than through the middle region. For non-wettable stripes oriented transversal to the direction of flow our simulations suggests that flooding of this region occurs, followed by rupture of the film, even for very large differences in chemical potential between the wettable and the non-wettable regions. The asymptotic regime (long times and large spatial scales) is analyzed using numerical solutions of the corresponding non-linear diffusion equation.

[1] M. N. Popescu and S. Dietrich, to appear in Proceedings of Computational Physics of Transport and Interface Dynamics Workshop, Dresden, February 17-March 8, 2002, edited by H. Emmerich, B. Nestler, and M. Schreckenberg, (Springer-Verlag, Heidelberg), in press.

[2] G. Oshanin, J. De Coninck, A.M. Cazabat, and M. Moreau, Phys. Rev. E.
58, R20 (1998)