Linear theory of particulate Rayleigh-Bénard instability

A two-fluid model is used to study the effect of point particles on the Rayleigh-Bénard stability threshold in a laterally unbounded cell. Equal particles are steadily and uniformly introduced at the top plate at their terminal velocity with a fixed temperature. Both velocity and temperature are allowed to vary while, falling, the particles interact with the fluid. This interaction is modulated by the ratio of the particle density and heat capacity to those of the fluid. Particles are found to have a stabilizing effect, which increases with their concentration and density up to several orders of magnitude above the single-phase stability threshold. This result is primarily a consequence of the particle mechanical, rather than thermal, coupling with the fluid. The particle initial temperature has a strong effect on the undisturbed temperature distribution in the cell, which is a significant factor for the stability of the system. The addition of particles greatly increases the dimension of the parameter space necessary to characterize the flow.