The importance of the fluid dynamics in the modelling of electrochemical systems is often underestimated. The knowledge of the flow velocity pattern in an electrochemical cell, in fact, can allow us to associate certain electrochemical reactions with specific fluid patterns to maximize the yield of some reaction and, conversely, to minimize unwanted or side reactions. The correct evaluation of the convective term in the Nernst-Planck equation, however, requires the solution of the so-called Navier-Stokes equations, and computational fluid dynamics (CFD) is today the established method to numerically solve these equations. In this work, a CFD model is employed to show that the gas-liquid flow pattern can be remarkably different in a single channel or in a multi-channel gas-evolving electrochemical system. In the single channel, in fact, under certain conditions, vortices and recirculation regions can appear in the flow, which does not appear in the multi-channel case. The reason of this difference is found in the uneven distribution of the small bubbles in the two cases. Additionally, a second, simplified, model of the flow is discussed to show how a higher concentration of small bubbles in the single channel system can destabilize the flow.