How small hydrodynamics can go

Understand

Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves.

• This phenomenon, labelled as "k-gap", could explain the surprising identification of a low-frequency elastic behaviour in confined liquids.
• More recently, a formal study of the perturbative hydrodynamic expansion showed that critical points in complex space, such as the aforementioned k-gap, determine the radius of convergence of linear hydrodynamics, its regime of applicability.
• In this work, we combine the two new concepts and we study the radius of convergence of linear hydrodynamics in "real liquids" by using several data from simulations and experiments.