# A simplified probabilistic model of self-propagating reactions in randomly layered nanolaminates

Journal Article

A simplified probabilistic model is developed of the transient evolution of self-propagating reactions in randomly-layered nanocomposites. We focus our attention on a class of mechanically formed nanocomposites, in which the probability density function (pdf) of the layering can be controlled in terms of the number of rolling passes. The unsteady evolution of self-propagating reactions in this class of randomly layered nanocomposites is described using a simplified physical model that combines a two-dimensional diffusion equation for the atomic concentration with a quasione-dimensional form of the energy equation which accounts for the melting of the reactants and products. The effect of random layering within the material is accounted for by discretizing the experimentally-generated bilayer pdf into a set of bins of finite width, and solving a decoupled system of diffusion equations that describe atomic mixing within idealized bilayers that correspond to the discrete bins. The diffusion equations are strongly coupled through a section-averaged energy equation, derived under the assumption that the temperature is uniform across the layers. Computations indicate that the resulting simplified probabilistic model provides reasonable predictions of the experimentally observed reaction velocities. The computations also yield useful correlations of the reaction velocity in terms of suitable moments of the bilayer pdf. Copyright © 2009 American Scientific Publishers All rights reserved.

### Full Text

### Duke Authors

### Cited Authors

- Knio, OM; Besnoin, E; Xun, Y; Lunking, D; Heerden, DV

### Published Date

- 2009

### Published In

### Volume / Issue

- 6 / 10

### Start / End Page

- 2298 - 2306

### International Standard Serial Number (ISSN)

- 1546-1955

### Digital Object Identifier (DOI)

- 10.1166/jctn.2009.1286