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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]