Simulation of reactive nanolaminates using reduced models: I. Basic formulation

Development and testing are described of a reduced model for the simulation of transient reactions in Ni/Al nanolaminates. The model relies on a simplified description of local atomic mixing rates, expressed in terms of an evolution equation for a dimensionless time scale that reflects the age of the mixed layer. The latter is obtained from a theoretical analysis of the quasi-1D evolution equation of a conserved scalar, which also yields canonical curves for the mean composition and its relevant moments as function of the local bilayer age. The reduced model is tested against results of the detailed model of Besnoin et al. [E. Besnoin, S. Cerutti, O.M. Knio, T.P. Weihs, J. Appl. Phys. 92 (2002) 5474-5481] for different scenarios, including self-propagating reactions, and ignition thresholds. Results show that the reduced model predictions are in good agreement with those obtained using the detailed model. By achieving order-of-magnitude increase in computation efficiency, the present model reduction formalism offers a path towards modeling transient reaction fronts in multiple space dimensions.