Hyperbolic regions in flows through three-dimensional pore structures.
Finite time Lyapunov exponents are used to determine expanding, contracting, and hyperbolic regions in computational simulations of laminar steady-state fluid flows within realistic three dimensional pore structures embedded within an impermeable matrix. These regions correspond approximately to pores where flow converges (contraction) or diverges (expansion), and to throats between pores where the flow mixes (hyperbolic). The regions are sparse and disjoint from one another, occupying only a small percentage of the pore space. Nonetheless, nearly every percolating fluid particle trajectory passes through several hyperbolic regions indicating that the effects of in-pore mixing are distributed throughout an entire pore structure. Furthermore, the observed range of fluid dynamics evidences two scales of heterogeneity within each of these flow fields. There is a larger scale that affects dispersion of fluid particle trajectories across the connected network of pores and a relatively small scale of nonuniform distributions of velocities within an individual pore.
University of Arizona, Program in Applied Mathematics, Tucson, Arizona 85721-0089, USA.
Jeffrey D
JD
Hyman
University of Arizona, Department of Hydrology and Water Resources, Program in Applied Mathematics, Tucson, Arizona 85721-0011, USA.
C Larrabee
CL
Winter