The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on nonuniform adaptive grids to study a series of nanoscale thin-film flows. The Fornberg scheme is used for high-resolution spatial discretization and a fully implicit time-marching scheme is designed for numerical stability. The accuracy of the numerical method is verified against theoretical results for thermal capillary waves during the linear stage of their development. The framework is then used to study the nonlinear behavior of three bounded thin-film flows: (1) droplet spreading, where power laws are derived; (2) droplet coalescence, where molecular dynamics results are reproduced by the SLE at a fraction of the computational cost and it is discovered that thermal fluctuations decelerate the process, in contrast to previously investigated phenomena; and (3) thin-film rupture, where, in the regime considered, disjoining pressure dominates the final stages of rupture.

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• Capillary waves
• Nanofluidics
• Thin fluid films