Dynamic dimension reduction for thin-film deposition reaction network models

Abstract

A prototype thin-film deposition model is developed and subsequently used in a sequence of model reduction procedures, ultimately reducing the dynamic dimension from six to one with essentially no loss in accuracy to the dynamics of the deposition process. The species balance model consists of a singular perturbation problem of nonstandard form which first is numerically solved following the approach of Daoutidis (2015). An alternative strategy then is presented, consisting of a reaction factorization procedure which facilitates the solution of the outer solution of the singular perturbation problem and provides unique physical insight into the conserved quantities (reaction invariants) identified by the elimination of redundant dynamic modes. Further reduction in dynamic dimension then is achieved through a second factorization focused only on the major reaction species. This second reduction procedure identifies pseudo- equilibria of finite-rate properties and introduces an additional level of complexity to the challenges of identifying consistent initial conditions for DAE systems.