title: Are continuum predictions of clustering chaotic?
abstract: Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ1≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a direct consequence of the fundamental kinematic instability, but requires a secondary (inherently multidimensional) instability.
authors.affiliation: Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: William D
authors.identifier: 0000000201427781
authors.initials: WD
authors.lastname: Fullmer
authors.affiliation: Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA.
authors.forename: Christine M
authors.initials: CM
authors.lastname: Hrenya