Long-wave interface instabilities of a two-layer system under periodic excitation for thin films

The stability of a system of two thin liquid films under AC electroosmotic flow is studied using linear stability analysis for long-wave disturbances. The system is bounded by two rigid plates which act as substrate. Boltzmann charge distribution is assumed for the two electrolyte solutions. The effect of van der Waals interactions in these thin films is incorporated in the momentum equations through the disjoining pressure. The base-state velocity profile from the present study is compared with simple experiments and other analytical results. Parametric study involving various electrochemical factors is performed and the stability behaviour is analysed using growth rate, marginal stability, critical amplitude and maximum growth rate in phase space. An increase in the disjoining pressure is found to decrease stability of the system. On the other hand, increasing the frequency of the applied electric field is found to stabilize the system. However, the dependence of the stability on parameters such as viscosity ratio, permittivity ratio, interface zeta potential and interface charge depends not only on the value of individual parameters but also on the rest of the parameters. Design of experiments (DOE) is used to observe the general trend of stability with different parameters.