A lot of effort has been made to manufacture metallic nanowires by topdown procedures as classical lithography. Metallic nanowire growth from solution represents a promising inexpensive bottom-up method working at room temperature. By applying an AC voltage, nanowires grow on a substrate between two electrodes in a solution containing metal complexes. Aiming at a controlled growth of straight and as thin as possible wires, the growth process is investigated both experimentally and theoretically. The nanowire itself, since it is conductive, is modeled as a half-sphere electrode. Our model includes the dielectrophoretic force on uncharged metal complexes as well as their diffusion in the solution. In particular, the growth velocity of the wire is found to depend only weakly on the applied voltage since the overall growth process is diffusion-controlled. Difficulties in comparing theoretical predictions and experimental observations due to poorly known material parameters are discussed. For reasonable parameter choices, the calculated nanowire growth velocity is in modest agreement with measurements.