Stability and rupture of nano-liquid film (NLF) flowing down an inclined plane

The two-dimensional flow of a nano-liquid film (NLF) down an inclined plane is represented by Navier–Stokes equation accounted for van der Waals and gravity forces. A long wave perturbation method obtains a non-linear evolution equation for the film interface. A linear theory for infinitesimal perturbation is derived to obtain an estimate of the film rupture time. The finite amplitude instability is quantified based upon numerical solution of the evolution equation using a finite difference technique. The predictions of the non-linear and linear theories are compared. van der Waals force play dominant role in the film rupture for lower thicknesses (≤100 nm), whereas gravity controls the instability in higher thicknesses (>100 nm). Effect of inclination becomes significant for films of thickness >100 nm. The growth of instability tends to be explosive near rupture, owing to excessive buildup of van der Waals attraction. Thus, it is shown that the van der Waals force is important in the dewetting of nano-liquid films.