Vorticity (top) and density (bottom) correlations resulting from odd viscosity in particle based hydrodynamic simulations (left) and experiments (right). The weak compressibility and the presence of a radial effective pressure resulting from odd viscosity amounts to density inhomogeneities $(\varphi (r)-\langle \varphi \rangle )/\langle \varphi \rangle ={\nu }^{\text{odd}}\omega /c^2$, where v^odd is the kinematic odd viscosity, and c is the propagation velocity of a colloidal density inhomogeneity. The density and vorticity plots show that areas of positive vorticity tend to be higher populated than the average density in the system, while the density in areas of negative vorticity tends to be lower. Averaging for each value of the density inhomogeneity over all given values of the corresponding vorticity reveals the linear relationship above, such that v^odd can be extracted from the measurement. In the presented system the odd viscosity at an area fraction of φ=0.075 is estimated as ${\nu }^{\text{odd}}\approx 1.5\times {10}^{-2}{\text{m}}^2/\text{s}$. Accordingly, density inhomogeneities resulting from odd shear stresses can only be perceived in long-lived vortical flows, since viscous stresses are transported much faster then odd shear stresses. Reprinted with permission from [34]. Copyright©2023 The Author(s).