Instability of nanofluid film flow under external electric field: Linear and weakly nonlinear analysis

This study investigates the instability of nanofluid thin films flowing down an inclined plane under the influence of a normal electric field. Based on the long-wave approximation and a systematic asymptotic expansion, a nonlinear evolution equation is derived to capture the coupled effects of the electric field and nanoparticle properties. Linear stability analysis reveals that the electric field enhances interfacial disturbances and promotes instability, whereas the presence of nanoparticles suppresses this effect by attenuating disturbance amplitudes. A weakly nonlinear analysis further clarifies the interplay among electric field strength, nanoparticle volume fraction, and density difference, enabling a classification of nonlinear stability regimes. Numerical simulations support the analytical predictions, showing that in unstable regimes, perturbations grow over time and eventually destabilize the film. These findings offer theoretical insights into the control of nanofluid film stability via electric field regulation and nanoparticle tuning.