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

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 -1012 P in the lowfrequency limit). The minimum quality factor Q for acoustic or tidal pressure oscillations is found to be typically -JOLJ03 arid occurs at a frequency w0 411'D'IIf, where D is the solute diffusivity and 'II is the number density of suspended inclusions of average radius f. For plausible parameter values, w0 is in the range of planetary interest (e.g. J0-4 Hz). At w .$ w0 , Q ex: w1; at w0 .$ w .$ Ds 2, Q ex: w; and at w ~ Ds2, Q ex: w'h. 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 105, needed to explain the volcanism of lo 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 0 S0 ) 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.