Universal G′ ∼ L–3 Law for the Low-Frequency Shear Modulus of Confined Liquids

Liquids confined to sub-millimeter scales have remained poorly understood. One of the most striking effects is the large elasticity revealed using good wetting conditions, which grows upon further decreasing the confinement length, L . These systems display a low-frequency shear modulus in the order of 1-10 3 Pa, contrary to our everyday experience of liquids as bodies with a zero low-frequency shear modulus. While early experimental evidence of this effect was met with skepticism and abandoned, further experimental results and, most recently, a new atomistic theoretical framework have confirmed that liquids indeed possess a finite low-frequency shear modulus G ', which scales with the inverse cubic power of confinement length L . We show that this law is universal and valid for a wide range of materials (liquid water, glycerol, ionic liquids, non-entangled polymer liquids, isotropic liquids crystals). Open questions and potential applications in microfluidics mechanochemistry, energy, and other fields are highlighted.