This work is devoted to the modeling of two phase flows arising in typical electrolysis devices. A numerical mixture model is used in order to resolve the two dimensional bubble plumes evolving along the electrodes. Plumes thickness sensitivity is studied for various parameters, such as bubble diameter, electrolyte viscosity, electrochemical cell geometry and current density. Using thermal buoyancy driven flow analogy, a dimensionless Rayleigh-like number Ram is defined to predict the behavior of the wall-bounded gas convection between two vertical facing electrodes. Different bubbles dispersion mechanisms are observed depending on two-phase flow dynamics and physical properties of the mixture. The effect of forced convection in the channel is also investigated. A scaling law for plume thickness evolution for a large range of Prandtl-equivalent number values is proposed. These results show that the bubble plume can be efficiently controlled by an imposed electrolyte velocity. (C) 2015 Elsevier Ltd. All rights reserved.