Shear and bulk viscosities of water up to 1.6 GPa and anomaly in the structural relaxation time

Abstract

Deep in the Earth's crust, pressure exceeds one thousand times the atmospheric pressure. Water still flows under these conditions, but experiences dramatic changes in structure and fluidity. Using combined dynamic and inelastic light scattering techniques, we simultaneously measure the shear and bulk viscosities of water as a function of pressure. The former increases faster than the latter, so that their ratio shows a two-fold decrease from 0 to 1.6 GPa; we confirm this trend with simulations. We analyze our results in terms of the structural relaxation time $τ$. Contrary to other liquids, pressure initially accelerates relaxation in water. Our measurements reveal that $τ$ reaches a minimum close to 1 ps around 0.5 GPa. We interpret $τ$ as a the equilibration time of hydrogen bonds, and propose that the minimum in $τ$ arises from a structural anomaly which allows fastest interconversion between local structures in water, and generates a cascade of thermodynamic and dynamic anomalies.

Figures (7)

• Figure 1: Shear viscosity of water as a function of pressure. This work: open circles for runs A (blue), B (red), C (black), D (purple), and E (green). The large and small symbols stand for data obtained with 100x and 50x objectives, respectively. Also shown are the data obtained with the rolling ball method abramson_viscosity_2007 (cyan stars), optical tweezers bowman_optical_2013 (magenta crosses), and a previous DDM attempt frost_isotope_2020 (orange diamonds). The solid and dotted black curves represent the IAPWS formulation for viscosity huber_new_2009 at 295.16K and its extrapolation above 1, respectively. The thick, dashed, gray curve is a $4^\mathrm{th}$ order polynomial fit to all our data, whose parameters are given in Supplementary Material (SM) SM.
• Figure 2: Bulk viscosity of water under pressure. Top panel: bulk viscosity as a function of pressure. Our results are shown with open circles for runs A (blue), B (red), C (black), D (purple), and E (green). The thick, dashed, gray curve is a second-order polynomial fit to all our data, whose parameters are given in SM. Ultrasonic data hawley_ultrasonicabsorption_1970 at 273.0, 283.3, and 303K are shown with magenta asterisks, pluses, and crosses, respectively. Bottom panel: ratio between bulk and shear viscosity as a function of pressure. The thick, dashed, gray curve shows the ratio of the respective fits to all our data (top panels of Figs. \ref{['fig:bulk']} and \ref{['fig:eta']}).
• Figure 3: Visco-elastic analysis. Top: comparison of relaxation times as a function of pressure. Analysis of the present Brillouin data with Eqs. \ref{['eq:visco1']}-\ref{['eq:visco3']} for individual measurements (open circles for runs A (blue), B (red), C (black), D (purple), and E (green)) and using the smooth fits to $\eta$ (Fig. \ref{['fig:eta']}) and $\alpha/f^2$ (Fig. \ref{['fig:attenuation']}) (solid curve); analysis with Eqs. \ref{['eq:visco1']}-\ref{['eq:visco3']} of ultrasonic data hawley_ultrasonicabsorption_1970 (magenta asterisks, pluses, and crosses at 273.0, 283.3, and 303K, respectively); and rotational relaxation time from NMR at 299K lang_high_1981 (grey pointed diamonds). Bottom: elastic moduli. The solid curves show $K_0$ from the equation of state theinternationalassociationforthepropertiesofwaterandsteam_revised_2018, and $K_\mathrm{r}$, $K_\infty$, and $G_\infty$ calculated from Eqs. \ref{['eq:visco1']}-\ref{['eq:visco3']} and smooth fits to $\eta$ (Fig. \ref{['fig:eta']}) and $\alpha/f^2$ (Fig. \ref{['fig:attenuation']}), or from the analysis of ultrasonic data hawley_ultrasonicabsorption_1970 (magenta asterisks, pluses, and crosses at 273.0, 283.3, and 303K, respectively). Adiabatic moduli for hexagonal ice gagnon_pressure_1988 are also shown: $K_\infty$ (purple hexagons) and $G_\infty$ (dashed curve).
• Figure 4: Lines of extrema in various properties of water. Extrema along isobars for density $\rho$ (dashdotted black curve), and along isotherms for shear viscosity $\eta$ (full red curve), self-diffusion coefficient D (short-dashed blue curve), and rotational correlation time $\tau_\theta$ (long-dashed green curve). The extrema are calculated with two-state models for experiments holten_entropy-driven_2012singh_pressure_2017 (top) and simulations of TIP4P/2005 water monterodehijes_viscosity_2018 (bottom). For real water, the purple ellipse in the top panel indicates the approximate location of the minimum in $\tau$ (see Fig. \ref{['fig:tau']}). For simulations, the bottom panel displays minima of the translational order parameter $t$agarwal_thermodynamic_2011 (purple discs). The gray dotted curves show the melting lines of the various ices for experiments wagner_new_2011 and simulations vega_what_2009.
• Figure 5: Comparison of shear viscosity data. Top panel: percent deviation of the experimental data from IAPWS formulation; only data up to the limit of validity of the formulation (1) are shown. Bottom panel: percent deviation of the experimental data from the fit to our data (see Fig. \ref{['fig:eta']}). Our results are shown with open circles for runs A (blue), B (red), C (black), D (purple), and E (green). The large and small symbols stand for data obtained with 100x and 50x objectives, respectively. Also shown are the data obtained with the rolling ball method abramson_viscosity_2007 (cyan stars), optical tweezers bowman_optical_2013 (magenta crosses), and a previous DDM attempt frost_isotope_2020 (orange diamonds).