A reactor comprising an inlet, an outlet, and a conically spiraling fluid flow channel coupled between the inlet and the outlet. The reactor may be an electrochemical reactor comprising a fluid flow channel that spirals about an axis, the fluid flow channel comprising an anode, a cathode across from the anode, and a membrane disposed between the anode and the cathode. The reactor may have a number of design parameters that are based upon one or more reaction species and that favor the occurrence of a reaction associated with the species. The reactor may be used for the electrolysis of water or for the production of other chemical products.