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This article reviews the mathematical and computer modeling of the process of ternary fluid mixture separation by free energy based phase field Lattice Boltzmann equations method. The process under study is considered in a limited area having the shape of a rectangle. Three different sets of fluid components with different structures are specified. The mathematical model constructed to describe this process is based on the Navier-Stokes equation for an incompressible fluid and the Cahn-Hilliard equation. The numerical model is built on the basis of LBM using the D2Q9 model. Numerical experiments were performed for two scenarios: (1) - investigate the model without gravity, in order to determine the patterns of the surface tension effect and (2) - investigate the model with gravity force. Numerical results showed a spinodal separation depending on the initial fractions of fluid concentrations. The results obtained determine the adequacy of the constructed model for a three-component fluid. [ABSTRACT FROM AUTHOR]

This article reviews the mathematical and computer modeling of the process of thermal phase transition in two-phase fluid flows. The nucleate boiling process is investigated in the presence of a constant heat source on a solid wall. Bubble formation and phase transition are taken into account. The flow characteristics and temperature distribution during nucleate boiling are obtained. The results of the numerical study were obtained using a 2D numerical algorithm implemented on the basis of the D2Q9 model of the Lattice Boltzmann method (LBM-Lattice Boltzmann method) and the phase field method. The calculations show that first the nucleation of a bubble is formed, then the bubble grows, breaks away from the boundary with the heat source, then, rising upward, undergoes deformation under the action of buoyancy forces. The effect of gravity and surface wettability on the bubble diameter during ascent is also numerically investigated. The results obtained are in good agreement with the experimental and numerical results of other authors. [ABSTRACT FROM AUTHOR]

In this work, a model of binary fluids with different densities and viscosities based on the solution of the Navier-Stokes equations, the continuity and the Cahn-Hilliard equation is developed. The process of influence of surface tension and interface thickness on the phase fields of fluids is investigated. The numerical results of the study are obtained on the basis of a phase field model using the lattice Boltzmann method (LBM). The LME uses two sets of distribution functions for incompressible flow: one for tracking the pressure and velocity fields and the other for the phase field. The use of the pressure distribution function can significantly reduce the effect of numerical errors in calculating the interfacial force. A several 2D tests are carried out to demonstrate the validation, which included droplet problem and the Raleigh- Taylor instability. It is shown that the proposed method allows tracking the interface with high accuracy and stability. [ABSTRACT FROM AUTHOR]