Electric current in two-dimensional systems with dominant electron-electron interaction have been predicted to show electric potential and current that deviates from the classical result of Ohms law. These systems are best described using low Reynolds number hydrodynamics, where the constitutive law is Stokes' law. It has been predicted that the electric current of such system with a geometry of an infinite strip with point source/sink contacts will display current vortices. We perform experiments on a low Reynolds number micro-fluidic finite width flow system that is analogous to the 2D electronic system, and observe the flow vortices corresponding to current vortices in the current strip.

Additionally, we calculate the electric current and potential of disk shaped system. We show that the electric potential demonstrates non-trivial patterns, different from those of the Ohmic case.

We use computational methods to obtain the electric potential and current for an ellipse shaped system, and we show that the appearance of vortices is dictated by the boundary conditions. We perform experiments on an ellipse shaped low Reynolds number micro-fluidic finite width flow systems and observe the flow vortices corresponding to the current vortices.