Purpose - The purpose of this paper is to the study the multiphase bubbles flow motion in a vertical channel with an electroconducting liquid without and under the influence of a magnetic field. Design/methodology/approach - For numerical calculations, the lattice Boltzmann method (LBM) is used, which is based on the kinetic theory for solving fluid mechanics and other physical problems. The phase-field lattice Boltzmann model is developed to simulate the behaviour of multiphase bubble-bubble interaction while rising in the fluid with high density ratios. Findings - The behaviour of the rising bubble flow in a rectangular column of two phases is investigated with the two-dimensional LBM. Originality/value - The multiphase flow in electroconducting liquids with high ratio of density is studied using the LBM.