Effect of Particle-to-Fluid Density Ratio on Stable-Unstable Transition in a Small-Scale Sedimentating Fluid-Solid System to Test the Limit of a Kinetic-Theory-Based Model

Kinetic-theory-based continuum models for gas-solid two-phase flow have been known to qualitatively predict the clustering instability for over a decade. More recently, quantitative analyses have been conducted to assess the accuracy of such predictions by studying the critical length scale necessary for the onset of clustering in a granular (no fluid) system (Mitrano et al. 2014). A similar approach is taken here for fluid-solid systems to study the effect of the particle-to-fluid density ratio in an unbounded, small-scale sedimentation (or fluidization) system. The Archimedes number is held at 71 and the solid volume fraction is varied between 0.1 and 0.4. As we increase the density ratio from 5 to 1000, the system makes a gradual transition from liquid-solid to gas-solid, and a variety of behaviors are observed: near-homogeneous at low density ratios, highly dynamic/chaotic at intermediate density ratios, and limit cycles in the form of a traveling wave at high density ratios. In each case, the type of flow behavior has a significant impact on the mean properties of the system. The sedimenting Reynolds number, which uses the vertical component of the solid-phase velocity as the velocity scale, is compared to LBM-DNS data of the same system. The results are good to favorable over a majority of the parameter space. However, at low density ratios the comparisons are not as good. It is suggested that this failure stems from the collision-dominated assumption inherent in the kinetic-theory approach, i.e., lubrication forces have been neglected in the continuum model. This hypothesis is tested using a Stokes-number criterion based on the fluctuating velocity (granular temperature), which shows that the largest errors do indeed occur where the underlying assumptions of the kinetic-theory-based model break down.