Anomalous Bulk Viscosity of Two-Phase Fluids and Implications for Planetary Interiors

Abstract

A calculation is presented for the irreversible entropy production that accompanies the imposition of a pressure perturbation on a two-phase medium consisting of a dilute suspension of one phase (as droplets or snowflakes) in another (liquid) phase of significantly different composition. No metastability is allowed, and the relaxation process is then dominated by the finite diffusivity of solute. The fluid medium behaves as though it has a very large bulk viscosity (typical value ∼10^(12) P in the low-frequency limit). The minimum quality factor Q for acoustic or tidal pressure oscillations is found to be typically ∼10^2–10^3 and occurs at a frequency ω_0 ∼ 4πDηS where D is the solute diffusivity and η is the number density of suspended inclusions of average radius S. For plausible parameter values, ω_0 is in the range of planetary interest (e.g. 10^(−4) Hz). At ω ≲ ω_0, Q ∝ ω^(−l); at ω_0 ≲ ω ≲ Ds^(−2), Q ∝ ω; and at ω ≳ Ds^(−2), Q ∝ ω^(½). The model is applied to helium rain clouds in the deep interiors of giant planets and is found to be capable in principle of providing a tidal Q ∼ 10^5, needed to explain the volcanism of Io and resurfacing of Enceladus. The model is also applied to the earth's outer core and found to be marginally capable of explaining the attenuation of radial modes (notably _oS_o) and potentially capable of providing significant attenuation of earth tides. However, quantification and application of the model are difficult because of large uncertainties in the nature of the required two-phase suspensions.

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