Novel energy-efficient desalination techniques, such as capacitive deionization (CDI), are a key element for the future of the fresh water supply, which is increasingly under stress due to the ever-growing world population and ongoing climate changes. CDI is a desalination technique where salt ions are removed from a flow channel by the application of an electrical potential difference across this channel and are stored in electrical double layers. The aim of this work is to visualize and explain the charging process of CDI using a new microfluidic approach. Namely, we implement the geometry of CDI on a chip and visualize the ion distributions in the channel using fluorescence microscopy. In contrast to normal CDI, our system was operated in the absence of flow, using non-porous electrodes. By using two pH-sensitive fluorescence dyes, we found the formation of pH waves across the channel, even though the system is operated at low potential differences in order to suppress Faradaic reactions, such as water splitting. From simulations of the transport process, we found that a small current density in the order of 0.1 A m-2 can trigger the formation of such pH waves. CDI generally benefits from large electrode areas relative to the channel cross section. However, this large area ratio will also increase the magnitude of these waves, which might lead to a reduction in desalination efficiency.