The stability of free convection in a particle-fluid mixture with a free surface

The onset of thermal instability for simultaneous surface tension and buoyancy driven mechanisms in a horizontal fluid layer with suspended particles is theoretically investigated by means of a small disturbance analysis. The critical Marangoni, Rayleigh and wave numbers are computed and compared with those known for a pure fluid. The effect of the particles enters through three parameters: gamma, phi and Gamma. The first describes how much particles are present, the second is determined by the particle-fluid thermal energy change ratio (named the heat loading ratio) and the third characterizes the size of the individual particles (the particle aspect ratio). It is found that when gamma or phi increases the system is destabilized while the raise of Gamma destabilizes or stabilizes the layer depending on whether the Rayleigh number is positive or negative.