Localized Scale Coupling and New Educational Paradigims in Multiscale Mathematics and Science.

摘要

One of the most challenging multi-scale simulation problems in the area of multi-phase materials is to develop effective computational techniques for the prediction of coalescence and related phenomena involving rupture of a thin liquid film due to the onset of instability driven by van der Waals or other micro-scale attractive forces. Accurate modeling of this process is critical to prediction of the outcome of milling processes for immiscible polymer blends, one of the most important routes to new advanced polymeric materials. In typical situations, the blend evolves into an emulsion of dispersed phase drops in a continuous matrix fluid. Coalescence is then a critical factor in determining the size distribution of the dispersed phase, but is extremely difficult to predict from first principles. The thin film separating two drops may only achieve rupture at dimensions of approximately 10 nm while the drop sizes are 0(10 im). It is essential to achieve very accurate solutions for the flow and for the interface shape at both the macroscale of the full drops, and within the thin film (where the destabilizing disjoining pressure due to van der Waals forces is proportional approximately to the inverse third power of the local film thickness, h-3). Furthermore, the fluids of interest are polymeric (through Newtonian) and the classical continuum description begins to fail as the film thins requiring incorporation of molecular effects, such as a hybrid code that incorporates a version of coarse grain molecular dynamics within the thin film coupled with a classical continuum description elsewhere in the flow domain. Finally, the presence of surface active additions, either surfactants (in the form of di-block copolymers) or surface-functionalized micro- or nano-scale particles, adds an additional level of complexity, requiring development of a distinct numerical method to predict the nonuniform concentration gradients of these additives that are responsible for Marangoni stresses at the interface.