Instability, rupture and fluctuations in thin liquid films: Theory and computations

Abstract

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction. The stochastic thin-film equation is also simulated by adopting a numerical scheme based on a spectral collocation method. The scheme allows us to explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we also study the effect of the noise intensity on the rupture time, which is in agreement with previous works.

23 pages, 8 figures, Published version J Stat Phys (2019)

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• Lattice Boltzmann simulations of stochastic thin film dewetting
• Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
• Thermal capillary waves on bounded nanoscale thin films
• Kinetic Monte Carlo and hydrodynamic modelling of droplet dynamics on surfaces, including evaporation and condensation
• Life and Death of a Thin Liquid Film
• Linear stability theory and molecular simulations of nanofilm dewetting with disjoining pressure, strong liquid-solid slip, and thermal fluctuations
• Surface tension of bulky colloids, capillarity under gravity and the microscopic origin of the Kardar-Parisi-Zhang equation
• Instability and rupture of sheared viscous liquid nanofilms
• Stochastic elastohydrodynamics of contact and coarsening during membrane adhesion