Onset of Triply-Diffusive Convection in a Fluid Layer with Suspended Particles and Temperature Dependent Viscosity

The present paper mathematically investigates the triply-diffusive convection problem with suspended particles by considering the viscosity to be temperature dependent. The temperature gradient is considered to be destabilizing whereas the solute gradients may be stabilizing or destabilizing. A sufficient condition for the validity of principle of exchange of stabilities (PES) is obtained and a bound for the complex growth rate of an arbitrary oscillatory perturbation, which may be neutral or unstable, is derived for this general problem. Various consequences of the above results are discussed and the analogous results under the individual effect of suspended particles, solute gradients and viscosity variations are also deduced.