Atomistic mechanisms of viscosity in 2D liquid-like fluids

Abstract

Shear viscosity plays a fundamental role in fluid dynamics from heavy-ion collisions to biological processes. Still, its microscopic mechanisms at the individual particle kinetic level remain a subject of ongoing research, specially in dense systems. In this work, we systematically investigate the shear viscosity ($η$) of two-dimensional (2D) simple fluids using computer simulations of Lennard-Jones, Yukawa, and one-component plasma systems. By combining Frenkel's liquid description, consisting of solid-like quasi-harmonic vibrations interrupted by thermally activated hops, with the concept of lifetime of local atomic connectivity $τ_{LC}$, we find a surprisingly simple formula for the kinematic viscosity that is solely determined by $τ_{LC}$ and the average kinetic particle speed $\bar{v}_p$. The derived analytical expression provides a direct link between macroscopic and microscopic dynamics, which shows excellent agreement with the simulation data in the dense liquid-like regime in all the 2D fluids considered. Moreover, it is discovered that, $τ_{LC}$ in 2D fluids is universally determined by the effective potential difference between the first peak and valley of the pair correlation function, implying a direct connection between macroscopic shear transport and microscopic structure. Finally, we demonstrate that the characteristic length scale $l_p= \bar{v}_p τ_{LC}$, which governs the macroscopic shear viscosity, aligns with the elastic length-scale that defines the propagation limit of collective shear waves in liquids. These findings establish that shear viscosity in 2D fluids arises from the diffusive transport of average particle momentum across the elastic length scale. Moreover, they highlight that shear dynamics are fundamentally governed by localized configurational excitations within the atomic connectivity network.

Figures (11)

• Figure 1: Viscosity, particle motion, and collective shear dynamics in liquids:(a) The shear viscosity $\eta$ determines the macroscopic resistance to shear flow in fluids. (b) A local configurational excitation consisting in losing or gaining one neighbor. $\tau_{LC}$, the lifetime of local connectivity, is the average timescale associated to this microscopic process. (c) Structural rearrangements in liquids are governed by localized events in which one or few particles hop a potential barrier ($\Delta G$), as assumed in Eyring and Frenkel theories of liquid viscosity. This activated process happens with an averaged rate $\tau_F^{-1}$, where $\tau_F$ is the microscopic Frenkel time. (d) Collective shear waves in liquids propagate only up to a length-scale $l\sim 1/k_g$, with $k_g$ the wave-vector gap in their dispersion. According to Maxwell viscoelasticity theory, $k_g \sim 1/(C_T \tau_M)$ where $C_T$ is the high-frequency speed of propagation for shear waves and $\tau_M$ is the collective Maxwell relaxation time.
• Figure 2: Microscopic origin of viscosity as diffusive transport of average particle momentum:(a) Dimensionless viscosity as a function of reduced temperature. (b) Dimensionless local connectivity time as a function of reduced temperature. (c) Test of the universal formula for viscosity proposed in Eq. \ref{['maineq']} of the main text.
• Figure 3: (a) Studied 2D L-J system at constant temperature. The colored symbols indicate the constant-temperature scans in the fluid phase. The background colors show the dynamical crossover (white) between the dilute gas-like phase (red) and the dense liquid-like fluid phase (blue). (b) Normalized viscosity as a function of the density at constant temperature. (c) Ratio of the high-frequency transverse speed of sound $C_T$ to the average particle speed $\bar{v}_p$ as a function of density. (d) Ratio between the viscosity obtained numerically using the Green-Kubo formalism ($\eta_{GK}$) and our theoretical formula Eq. \ref{['maineq']} ($\eta_{LC}$) as a function of density $n$. The same background color scheme is used in all panels.
• Figure 4: Bridging collective shear dynamics to particle-level motion:(a) Spectra of transverse modes in a 2D Yukawa liquid-like fluid with $\kappa=1$, and the corresponding dispersion relation marked as dots. Frequencies are normalized by the nominal dusty plasma frequency $\omega_{pd}\equiv \left(Q^2/2\pi m \epsilon_0 m a^3\right)^{1/2}$PhysRevLett.92.065001, while wave-vectors are normalized using the Wigner-Seitz radius $a$. The obtained dispersion relations under different reduced temperatures are presented in the inset. (b) Same analysis for 2D L-J liquid-like fluids with particle density $n=1$ at different reduced temperatures $T/T_m$. (c) Universal linear relation between the dimensionless cutoff wave-vector $k_g$ and the inverse dimensionless microscopic length-scale $l_p=\bar{v}_p \tau_{LC}$. The slopes of the two fitting lines are $\approx 0.98$ and 0.88, respectively.
• Figure 5: Structural definition of the local connectivity time:(a) Calculated pair-correlation function $g(r)$ of a 2D L-J liquid (red line) and the corresponding effective potential $w(r)/k_B T$ (blue dashed line). The vertical black arrows indicate the potential difference between the first maximum and first minimum that is identified with the potential barrier $\Delta G$ in Frenkel's description, Eq. \ref{['pot']}. (b) The temperature dependence of the potential factor $\exp\left(\Delta w /k_B T\right)$ as a function of the reduced temperature $T/T_m$ for the various systems studied. (c) The universal linear relation between the dimensionless local connectivity time $\tau_{LC}/\left(n k_B T / m \right)^{-1 / 2}$ and $\exp\left(\Delta w/k_B T\right)$ for all systems considered.