Emergence of quantized vortices in microfluidic devices

Structured vortices in microfluidic flows are often associated with suspensions of active matter that move in a collective fashion. For instance, vortical flows at microscales have been observed in bacterial swarms, with their forming mechanisms attributed to the self-propulsion of individuals and the cell-cell interactions. Here, we demonstrate that an array of microscale vortices can emerge purely due to the geometry and dimensionality in a steady flow. Specifically, we show that a chain of vortices can be induced in a rectangular cavity that is sheared under a steady flow. Interestingly, these vortices have an intrinsic aspect ratio, with their numbers quantized by the length of the cavity. We also elucidate that such intrinsic flow structures can be generalized to a wide class of confining geometries, indicating a fundamental mechanism of vortex formation in microscale flows.