The onset of long-wave oscillatory thermosolutal instability in a heated layer of a moderately dense nanofluid

We investigate the thermosolutal Marangoni instability in a moderately dense nanoparticle suspension (nanofluid). The nanofluid layer deposited on a solid substrate and subjected to a specified constant heat flux is exposed to the ambient atmosphere at the air–liquid deformable interface. The effects of thermophoresis and gravity are considered. Using the method of asymptotic expansions, we investigate the oscillatory long-wave thermosolutocapillary instabilities, taking into consideration the dependence of the thermophysical properties of the nanofluid on the local nanoparticle concentration. Variations in the threshold of the long-wave oscillatory thermocapillary instability with the heat transfer rate at the interface and the interface deformability are obtained. We find a transition from monotonic to oscillatory thermosolutal Marangoni instability with a codimension-two point bifurcation. An excellent agreement is obtained between the results of the asymptotic analysis and those of the numerical solution of the full eigenvalue problem, in terms of the critical values of the Marangoni number, the wavenumber, and the frequency.