The effect of slip and inertia on the instability of bounded films: Linear instability and arbitrary-order lubrication theory

Higher-order lubrication equations are derived for the van der Waals force driven dynamics of liquid films on slip substrates. Linear stability analysis is performed to evaluate the accuracy of the higher-order lubrication models and the classical lubrication models. By providing a more accurate asymptotic representation of the velocity field, the higher-order models overcome limitations of the classical lubrication equations, whose validity is typically restricted to specific slip regimes. The analysis further shows that, in the viscosity-dominated regime, increasing slip length accelerates film rupture and promotes larger-scale dewetting patterns. In the inertia-dominated regime, by contrast, the influence of slip is reduced because stronger inertia leads to a thinner boundary layer. Furthermore, the 3rd-order lubrication equations are solved numerically. Compared with the Navier–Stokes equations, the lubrication models significantly improve computational efficiency without sacrificing the essential information on interface evolution and velocity field structure.