The onset of anomalous solutocapillary instability in an isothermal nanofluid layer with interfacial kinetics

We investigate the emergence of an anomalous solutocapillary instability in an isothermal nanofluid layer with a non-deformable liquid–gas interface. A model of the equation of state for the colloidal suspension is presented. The surface tension exhibits non-monotonic variation with nanoparticle concentration due to nanoparticle surface energetics. In what follows, we consider nanoparticle interfacial kinetics and express the dynamics of surface concentration via the spatio-temporal evolution equation. We analyse the linear stability around the quiescent base state using normal modes and deduce the linear eigenvalue problem to determine the growth rates of these modes. The analytical solution for the monotonic solutocapillary instability is found. Surprisingly, the system displays the onset of an anomalous short-wave solutocapillary instability due to an increase in surface tension with the particle concentration.