Obstacle Lattices

This chapter explores the impact of placing small obstacles in the flow field of a microswimmer suspension. As recently shown in experiments, appropriate arrangements of obstacles can organize the turbulent flow into vortex lattices with different geometric properties. Based on the reduced minimal model we show the stabilization of square and triangular structures as well as a more exotic chiral pattern in a Kagome-like arrangement that displays spontaneous symmetry-breaking and large-scale circulatory flows. To explore the transition between order and disorder in these stabilized vortex structures, we take a closer look at the square lattice. Mapping the system to an antiferromagnetic spin lattice, we uncover intriguing parallels to the Ising model and its universality class, including an effective temperature proportional to the strength of nonlinear advection.