The results of numerical modeling of two-phase electrolyte thermo-and hydrodynamics in the working space of a separate electrolyzer cell with vertical electrode arrangement are presented. The problem is solved in a self-consistent formulation taking into account the electric current, Joule heat evolution, gas evolution, gas and liquid flows, and electric conductivity of the disperse phase. Within the framework of the proposed two-liquid approach, near-wall bubbly flow is calculated using a model of expanding gas plume, which is based on the introduction of an effective force acting upon the gas phase. The results of several variants of such calculations are compared. The numerical solution is also compared to approximate analytical solutions of the problem. The results of this study can be used to calculate estimations of the electrical and thermal regimes of vertical electrolyzers.