Reducing the concentration of hydrogen and oxygen dissolved in the electrolyte helps to increase the efficiency of alkaline water electrolysis. This thesis provides an account of the evolution of dissolved concentration in the vicinity of the electrode surface for alkaline water electrolysis for the bubble size, the electrode height, the dissolved gas uptake by bubbles, and the bubble generation at the electrode surface. Included are an analytical and numerical model that not often include local electrokinetic effects coupled with a gas-liquid flow model. As is commonly found for experimental data on dissolved hydrogen and oxygen, the dissolved species is either an average concentration measured relatively far from the electrode surface or an average concentration at the electrode surface without any local effect of the electrode kinetics. In this thesis an agreement is found for the analytical derived natural convection up to an height of 0.01 [m] with the numerical model. The fraction of dissolved hydrogen and oxygen taken up by the gas bubbles is enhanced for smaller bubbles, a high frequency of bubbles generated, and an increased mass transfer of dissolved gas at the electrode. Moreover, a clear difference is found for the dissolved hydrogen and oxygen evolution near the electrode for horizontal and vertical electrodes. Horizontal electrodes have more dissolved gas at the electrodes, likely due to the dissolved gas not being able to transfer to the gas bubbles as easily for vertical electrodes. Also, for both vertical and horizontal electrodes the dissolved gas concentration flattens for increased current density, likely due to homogeneous nucleation. For an increasing electrode height a lowering of the dissolved gas was observed, associated with an increased dissolved gas uptake by the bubbles. Most of these local effects are able to be modelled using an analytical and numerically combined model. These simulations greatly improve the understanding of dissolved hydrogen and oxygen evolution in the vicinity of electrodes.