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Abstract

The mean flow and the linear stability characteristics of a two-dimensional particulate suspension, driven horizontally via harmonic oscillation, are analyzed. A constitutive model based on the kinetic theory of granular materials, which takes into account the dissipative collisional interactions among particles as well as their interactions with the interstitial fluid, is used; the effects of the interstitial fluid are incorporated in the balance equations for the particle phase. Assuming that the suspension is thin along the vertical direction, the effects of driving are incorporated into the governing equations in a mean-field manner. Using Floquet theory, a linear stability analysis of the time-periodic mean flow indicates that the oscillatory suspension supports stationary- and traveling-wave instabilities which correspond to particle banding patterns that are aligned parallel or orthogonal or at an oblique angle to the driving direction. The effects of external driving parameters and various system control parameters on the phase diagram of instabilities are studied. The fluid-particle interaction is shown to be responsible for the emergence of traveling instabilities in this flow.