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Title: Molecular hydrodynamics: Vortex formation and sound wave propagation

Abstract

In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecularmore » scale.« less

Authors:
ORCiD logo [1];  [2];  [3];  [4]; ORCiD logo [1]
  1. Korea Advanced Inst. Science and Technology (KAIST), Daejeon (Korea, Republic of)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  3. Univ. Augsburg (Germany)
  4. Brown Univ., Providence, RI (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory, Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1435106
Alternate Identifier(s):
OSTI ID: 1416644
Grant/Contract Number:  
AC02-05CH11231; AC05-00OR22725
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 148; Journal Issue: 2; Related Information: © 2018 Author(s).; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Karniadakis, George Em, and Lee, Eok Kyun. Molecular hydrodynamics: Vortex formation and sound wave propagation. United States: N. p., 2018. Web. doi:10.1063/1.5011992.
Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Karniadakis, George Em, & Lee, Eok Kyun. Molecular hydrodynamics: Vortex formation and sound wave propagation. United States. doi:10.1063/1.5011992.
Han, Kyeong Hwan, Kim, Changho, Talkner, Peter, Karniadakis, George Em, and Lee, Eok Kyun. Sun . "Molecular hydrodynamics: Vortex formation and sound wave propagation". United States. doi:10.1063/1.5011992. https://www.osti.gov/servlets/purl/1435106.
@article{osti_1435106,
title = {Molecular hydrodynamics: Vortex formation and sound wave propagation},
author = {Han, Kyeong Hwan and Kim, Changho and Talkner, Peter and Karniadakis, George Em and Lee, Eok Kyun},
abstractNote = {In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.},
doi = {10.1063/1.5011992},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 2,
volume = 148,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 1 work
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Figures / Tables:

FIG. 1 FIG. 1: Velocity field u(x, t) at t = 4. The flow patterns obtained from MD simulations are presented in panels (a)–(c) in an increasing order of system size, N = 512, 1024, and 2048 (L = 29.2, 41.3, and 58.4). The entire domain is divided into cells of sidemore » length ∆xvel = 2 and the average velocity of each cell is depicted by an arrow, which is colored depending on the log scale of its magnitude. The red dot at the center denotes the initial position of the tagged particle. The three contours with red solid lines depict regions within which the tagged particle is found at probabilities 0.5 (inner), 0.9 (middle), and 0.99 (outer). The vector fields for the two small system sizes clearly exhibit visible deviations from periodicity at the boundaries. Only for the largest system, the flow field generated by the tagged particle does not yet cover the full square and hence is not influenced by the finite system size at time t = 4.« less

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