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At the solid-liquid interface, a charge zone called the Electrical Double Layer (EDL) appears. It is constituted of two zones of opposite sign, one in the solid and another one in the liquid. When a liquid flows through a pipe, there is a disturbance of the EDL and an axial streaming current is generated. This current is due to the convection of the charges coming from the electrical double layer. In this paper, we present a numerical simulation of the EDL development process in the case of a liquid containing additives or impurities which are partially dissociated into positive and negative ones. We treat the case of laminar flow and an interfacial reaction whose conversion is small compared to the concentration of positive and negative ions in the bulk solution. The boundary conditions are deduced from the kinetics of the wall surface reactions with additives. However, in this paper, the formation of the EDL at the solid-liquid interface is investigated without any flow (static case). Thus, the rate of the wall reaction and the resulting charge concentration in the liquid can be studied. Then, once the equilibrium of physicochemical reaction is reached, convection is forced and the EDL dynamic behavior has been studied (dynamic case). The physicochemical reaction at the solid-liquid interface, the evolution of the space charge density in terms of both the axial coordinates and flow velocity, and the equations of conservation of charge of the liquid species have been implemented to a developed version of "Electricite de France" finite volume CFD tool Code_Saturne, which is designed to solve the Navier- Stokes equations. Finally, the simulation results of the dynamic behavior at different flow rates are compared with the experimental results.