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In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism, one introduces an order parameter called phase-field function to characterize thermodynamically the phases. All the system parameters are assumed to vary continuously from one fluid bulk to another (as linear functions of the phase-field). The Navier-Stokes equation (with some extra terms) and the heat equation are written only once for the whole system. The evolution of the phase-field is described by the Cahn-Hilliard equation. In the sharp-interface limit the results found by the phase-field formalism recover the results given by the classical formulation.
We show that a laser beam which propagates through an optical medium with Kerr (focusing) and higher order (defocusing) nonlinearities displays pressure and surface-tension properties yielding capillarity and dripping effects totally analogous to usu
We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolut
Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrodinger (NLS) model in $(2+1)$-dimensions. We identify an analogue of surface tension in optics, namely a single parameter depending on the degree of nonlocal
A thin-film model for a meniscus driven by Rayleigh surface acoustic waves (SAW) is analysed, a problem closely related to the classical Landau-Levich or dragged-film problem where a plate is withdrawn at constant speed from a bath. We consider a mes
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a harmonic modula