  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. We generically show that the radius of
convergence increases with temperature and it surprisingly decreases with the
electromagnetic interactions coupling. More importantly, for all the systems
considered, we find that such radius is set by the Wigner-Seitz radius, the
characteristic inter-atomic distance of the liquid, which provides a natural
microscopic bound.
