Thermosolutal instabilities in a moderately dense nanoparticle suspension

We investigate the onset of thermosolutal instabilities in a moderately dense nanoparticle suspension layer with a deformable interface. The suspension is deposited on a solid substrate subjected to a specified constant heat flux. The Soret effect and the action of gravity are taken into account. A mathematical model for the system considered with nanoparticle concentration-dependent density, viscosity, thermal conductivity and the Soret coefficient is presented in dimensional and non-dimensional forms. Linear stability analysis of the obtained base state is carried out using disturbances in the normal mode, and the corresponding eigenvalue problem is derived and numerically investigated. The onset of various instabilities is investigated for cases of both heating and cooling at the substrate. The monotonic solutocapillary instability is found in the case of cooling at the substrate, which exhibits two competing mechanisms that belong to two different disturbance wavelength domains. We identify the occurrence of both monotonic and oscillatory thermocapillary instabilities when the system is heated at the substrate. Furthermore, we show the emergence of the solutal buoyancy instability due to density variation which is promoted by the Soret effect adding nanoparticles heavier than the carrier fluid in the proximity of the layer interface. Transitions from the monotonic to oscillatory thermocapillary instability are found with variation in the gravity- and solutocapillarity-related parameters. Notably, we identify a previously unknown transition from monotonic to the oscillatory thermocapillary instability due to the variation in the strength of the thermal-conductivity stratification coupled with the Soret effect.