Thermosolutal instabilities in a moderately dense nanoparticle suspension in the presence of interfacial kinetics: the case of cooling at the substrate

We investigate the onset of thermosolutal instabilities in a layer of moderately dense nanoparticle suspension cooled at the substrate in the presence of interfacial nanoparticle kinetics (adsorption and desorption) at the deformable interface. Gravity and the Soret effects are taken into account. A mathematical model with nanoparticle concentration-dependent thermophysical properties of the nanofluid is formulated. The surface tension is assumed to be a linear function of the temperature; however, the equation of state displays non-monotonicity with nanoparticle concentration due to nanoparticle interfacial energetics. We carry out the linear stability analysis of the quiescent base state using normal modes and the obtained eigenvalue problem is solved numerically. The monotonic short-wave solutocapillary instability is found and analysed for different parameter sets. The limiting case of insoluble interfacial nanoparticle concentration is also investigated. Notably, we identify the onset of the monotonic short-wave thermocapillary instability owing to a strong coupling between the perturbations of interfacial nanoparticle concentration and temperature via the particle concentration-dependent thermal conductivity in general, and in particular, near the interface. The combined thermo-solutocapillary instability is also investigated. Finally, the simplified toy problem is formulated and solved analytically to demonstrate the role of thermal conductivity stratification and interfacial kinetics.