Fluctuations, hydrodynamics and scale separation in gas–solid flows

Fluctuations in the number of particles (or droplets and bubbles) are observed in experiments of multiphase flows, and these also manifest as fluctuations of the dispersed–phase volume fraction. The intensity of these fluctuations is characterized using a mathematical description based on second–order statistics. The intensity and range of fluctuations in the clustering regime of a granular gas is characterized using hard–sphere simulations. The influence of these fluctuations on conservation laws is first investigated through the hydrodynamic equations that arise in the standard average number density representation in kinetic theory of granular and gas-solid flow. The effect of number fluctuations on the unclosed conditional acceleration term in the kinetic theory of gas–solid flow is examined using data from particle–resolved direct numerical simulation. The intensity and range of fluctuations suggest a breakdown of scale separation that underlies continuum descriptions of gas–solid flow, such as the two–fluid theory and the first–order hydrodynamic description that arises from the Boltzmann–Enskog approach to gas-solid flow. Fluctuation hydrodynamics of gassolid flow is proposed as a route to rigorously incorporate the effect of fluctuations on conservation laws at both the first and second–order levels of description.