Confinement-Induced Diffusive Sound Transport in Nanoscale Fluidic Channels

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Confinement-Induced Diffusive Sound Transport in Nanoscale Fluidic Channels

Hannes Holey, Peter Gumbsch, and Lars Pastewka

Phys. Rev. Lett. 131, 084001 – Published 21 August 2023

Abstract

Molecular dynamics (MD) simulations have been widely used to study flow at molecular scales. Most of this work is devoted to study the departure from continuum fluid mechanics as the confining dimension decreases. Here, we present MD results under conditions where hydrodynamic descriptions typically apply, but focus on the influence of in-plane wavelengths. Probing the long wavelength limit in thermodynamic equilibrium, we observed anomalous relaxation of the density and longitudinal momentum fluctuations. The limiting behavior can be described by an effective continuum theory that describes a transition to overdamped sound relaxation for compressible fluids.

Received 5 January 2023
Accepted 18 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.084001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Acoustic wave phenomena Channel flow Fluctuations & noise Laminar flows Lubrication theory Nanofluidics Thin fluid films

Molecular dynamics Navier-Stokes equation Stokes equations

Fluid DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Hannes Holey ^1,2,*, Peter Gumbsch ^1,3, and Lars Pastewka ^2,4,†

¹Institute for Applied Materials, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany
²Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany
³Fraunhofer Institute for Mechanics of Materials IWM, Wöhlerstraße 11, 79108 Freiburg, Germany
⁴Cluster of Excellence livMatS, Freiburg Center for Interactive Materials and Bioinspired Technologies, University of Freiburg, Georges-Köhler-Allee 105, 79110 Freiburg, Germany

^*hannes.holey@kit.edu
^†lars.pastewka@imtek.uni-freiburg.de

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Issue

Vol. 131, Iss. 8 — 25 August 2023

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Images

Figure 1
Molecular dynamics simulation setup of a Lennard-Jones fluid confined between rigid walls. One of the lateral dimensions of the system is much larger than the gap height.
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Figure 2
Autocorrelation functions of density and longitudinal momentum fluctuations in a supercritical fluid for three modes, with the largest wavelength corresponding to $k_{1} σ = 4.45 \times 10^{- 3}$ . The inset shows the long-time behavior of density correlations on a logarithmic axis as well as the theoretical expression for the $k_{1}$ mode of an equivalent bulk fluid (dotted line).
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Figure 3
Dispersion relation for a height-averaged continuum formulation of confined fluids. Solid and dotted lines describe the angular frequency using the magnitude of the phase velocity with [Eq. (5)] and without long wavelength approximation, respectively. The dashed line describes the bulk reference. The wave number is normalized by $k_{crit} = 6 ν / h^{2} κ c_{T}$ and the angular frequency is normalized by the characteristic relaxation time of longitudinal modes in the underdamped limit $\lim_{k \to k_{crit}} τ_{∥} = h^{2} κ / 6 ν$ . The critical transition from underdamped to overdamped dynamics occurs with diverging group velocity.
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Figure 4
Comparison of longitudinal momentum fluctuations in bulk and confined LJ liquids. Sound frequency and attenuation constants are obtained from a fit to autocorrelation functions at various wavelengths, e.g., as shown in panel (a) and (b). The sound velocities (c) and relaxation times (d) are then compared to the theoretical predictions from Eqs. (5) and (7b), respectively. Viscosity and speed of sound are computed from separate bulk equilibrium simulations, and nonequilibrium MD simulations have been performed to obtain the slip length. The continuum model describes the MD data reasonably well. Deviations between the model and the data at small wavelengths are due to effective viscosity enhancement in the confined system compared to the bulk. Lowering wall-fluid interaction energies leads to a better agreement in the low wavelength regime, as shown by the open diamonds in panel (d). Transition to overdamped behavior is expected for wavelengths larger than $914.3 σ$ . Note that the speed of sound measured from MD is adiabatic ( $c_{s}$ ) rather than isothermal ( $c_{T}$ ).
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Figure 5
Sound relaxation times obtained from fits to the autocorrelation functions of longitudinal momentum and density fluctuations in the supercritical LJ fluid. Bulk and underdamped behavior is similarly described as in Fig. 4, but the lower critical wavelength ( $λ_{crit} = 689.3 σ$ ) allows easier exploration of the overdamped regime. Upwards and downwards pointing triangles are fitted density and longitudinal momentum relaxation times, respectively.
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