Self-organized Vortex Structures of Three-dimensional Electroconvection in a Confined Geometry

Here, we describe the first laboratory visualization of 3D Electroconvection (EC; a hydrodynamic instability) in confined geometries, a scenario often found in many electrochemical systems with internal flows bounded in narrow channels. Combining experiment and numerical modeling in a confined structure composed of identical ion exchange membranes at the top and bottom and a non-permeable polygonal sidewall, we figured out that the vortex boundary of EC is always formed perpendicular to the sidewall to minimize frictional energy loss. If this wall effect becomes dominant as the aspect ratio of the channel decreases and/or the voltage increases, we observed a self-organized vortex structure by converging the vortices from the sidewalls at the center of the channel. In this condition, the number of vertices of the confined wall determines the number of self-organized vortices; e.g., 3 vortices in a triangular channel. When we contained the EC in a circular channel with an infinite number of vertices, the number of self-organized vortices can be adjusted with respect to the applied voltage. On the other hand, if the aspect ratio increases and/or voltage decreases, a group of polygonal vortex patterns was developed, and a few vortices on the sidewall have a perpendicular boundary.