Global geometry and coarse-grained formulation of the evolution of pointwise intermaterial interface measure in chaotic flows

The article develops a coarse-grained model for the evolution of the intermaterial contact interface measure (length in 2d, area in 3d) in chaotic flows, starting from the global geometric properties characterizing these flows. The model reduces to a finite-volume formulation for the balance equations expressing the evolution in time and space of the interface measure, where its local growth rate within chaotic regions is controlled by the average (D(x, t) : e(u)(x, t)), D(x, t)), D(x, t) being the deformation tenser and e(u)(x, t) the unit vector spanning the unstable invariant subspace at the point x. The analysis is developed for two- and three-dimensional flows, and is useful not only for short-cut analysis of interface measures but also as a tool in the development of coarse-grained models of reaction/diffusion kinetics in chaotic flows accounting for the complex lamellar structure generated in such systems. (C) 2001 Elsevier Science Ltd. All rights reserved.