When a fluid flow is imposed on a porous medium, the infiltration flow may interact with the reaction-induced porosity variations within the medium and may lead to fingering instabilities. A nonlinear model of such interaction is developed and morphological instability of a planar dissolution front is demonstrated using a linear stability analysis of a moving-free-boundary problem. The fully nonlinear model is also examined numerically using finite-difference methods. The numerical simulations confirm the predictions of linear stability theory and, more importantly, reveal the growth of dissolution fingers that emerge as a result of these instabilities.

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Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10 −14 s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.