Auto-model based computer simulation of Plateau–Rayleigh instability of mixtures of immiscible liquids

Abstract

The classic theory to derive the characteristic Rayleigh wavelength, i.e., the distance between neighbouring droplets into which an originally cylindrical liquid body disintegrates, as a consequence of Rayleigh instability, is analysed in terms of the phenomenon of self-organization due to the mechanism of ‘fastest forming instability’. The paper aims at simulating this self-organization with Monte Carlo dynamics while accounting spatial interactions in lattices of Markov Random Fields that enable also modelling of Plateau–Rayleigh instability of instable mixtures of dispersed immiscible liquids. The Hammersley and Clifford theorem, concerning the general form of energy function, belonging to Markov Random Fields, is introduced for detailed classification of a simple model used for computer simulation. The relevant Auto-model, with Kawasaki dynamics, is chosen to investigate the liquid jet and the instability of the liquid’s cylindrical film. The computer-simulated outputs show encouraging agreement with the classic analytical predictions on main features of the Rayleigh instability. The model is also used as a foundation stone for developing a simple analytical approach for the estimation of Rayleigh wavelength of jets and cylindrical films, composed of instable mixtures of immiscible liquids. Qualitatively, the theory agrees with both computer simulation and experiment.