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Mathematical Modeling, Simulation, and Analysis of Two Problems in Interfacial Fluid Dynamics

We consider two problems in low Reynolds-number, interfacial fluid mechanics: the rupture of thin liquid films on chemically-patterned solid substrates, and the engulfment of foreign particles by a solidification front progressing through a binary alloy.

analysis of the evolution equation, we find that substrate patterning leads to a
resonance effect, causing the steady states of the film to undergo an imperfect
bifurcation. We will obtain predictions for film shapes, stability, growth rates, and ...