Mizuno H, Yamamoto R. General constitutive model for supercooled liquids: anomalous transverse wave propagation.
PHYSICAL REVIEW LETTERS 2013;
110:095901. [PMID:
23496725 DOI:
10.1103/physrevlett.110.095901]
[Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2012] [Indexed: 06/01/2023]
Abstract
A transverse acoustic wave propagates through supercooled liquids in an anomalous manner: for a macroscopic wave number k, the wave propagates long distances, as in elastic solids, whereas it attenuates rapidly for a mesoscopic to microscopic wave number k, as in viscous liquids. In this work, we theoretically describe this anomalous wave propagation using the hydrodynamics of the two-mode Maxwell constitutive model, which were determined independently from the mechanical properties under oscillatory shear strains. To ensure that the Maxwell model can be applied down to a microscopic length scale, we extended it to a k-dependent equation, taking into account the recently reported k dependences of the shear viscosity and modulus [A. Furukawa and H. Tanaka, Phys. Rev. Lett. 103, 135703 (2009); A. Furukawa H. Tanaka Phys. Rev. E 84, 061503 (2011)]. The anomalous wave propagation in supercooled liquids can also be understood in terms of a linear coupling of many independent normal modes, as in amorphous solids.
Collapse