  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, $\lambda_1 \approx 1/\tau$, 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 result of the fundamental kinematic instability, but
of the secondary (inherently multidimensional) instability.
