Effects of settling thermal inertial particles and bubbles on the hydrodynamic stability of the Rayleigh-Bénard system

In this study we explore the dynamics of particulate matter on the onset Rayleigh-Bénard (RB) convection. Heavy particles are injected from the top with the cold wall temperature, while light particles are injected from the bottom with the hot wall temperature. For the particulate phase we take into account the viscous (Stokes drag)  and inertial hydrodynamics forces (pressure gradient and added mass) on the particles as well as the buoyancy force. Furthermore, the particles are also thermally coupled to the fluid as they have a proper thermal diffusivity and specific heat capacity.  The particle properties are parametrized by the added-mass adjusted density-ratio β (which varies in the range [0,3], particle diameter φ, particle injection temperature θ*_p, and fluid/particle heat capacity ratio E. The two-fluid model is used to investigate the thermal and mechanical interplay between particles and fluid flow. 

We present the results of a linear stability analysis for the onset of convection in this particulate RB system, focusing on the effect of the particle mass density parameter β. This study extends previous investigations by Prakhar & Prosperetti [1] limited to the case of very heavy particles.  Remarkably, both heavy and light particles stabilize the system with respect to the single-phase RB threshold, while the case β = 1 of neutrally buoyant particles has a negligible effect on the system. It is found that, similarly to the single-phase RB setting, the system undergoes always a pitchfork bifurcation giving rise to stationary convection patterns (that however can have different wave numbers with respect to the ones in classical RB). The particle thermal coupling acts as an extra stabilization factor, with a weak dependence on the injected temperature. This theoretical research suggests ways to control thermal heat transfer by a vertical injection of a particulate phase. It prompts to future studies with either numerical or experimental approaches to validate the present findings and explore more extensively the system parameter space.

Refrences:

[1] Prakhar, S. & Prosperetti, A. Linear theory of particulate Rayleigh-B.nard instability., Physical Review Fluids. 6, 083901 (2021).