A modeling methodology based on the coupling of free surface energy minimization techniques and
computational fluid dynamics (CFD) modeling has been developed for simulating the macro-regime of evaporation-driven
self-assembly processes; specifically, those processes that use lithographically defined features to precisely direct
the self-assembly of particles on a substrate. Because surface tension dominates the gravitational, inertial, and viscous
forces acting on the droplet, the shape of the droplet is determined as a function of its volume and pinning geometry by
minimizing its surface energy. The evolution of droplet shape during evaporation is used to define the deforming
control volume, over which the governing partial differential equations for conservation of mass, momentum, and
particle concentration are solved. By decoupling the free surface and the flow models, a diverse range of problems can
be investigated. The macro-scale model is envisioned as one part of a hierarchical model that can be used to study the
entire lithographically-directed, evaporation-driven self-assembly process.
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