• Kieffer S
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The sound speed of a two-phase fluid, such as a magma-gas, water-air,
or water-steam mixture, is dramatically different from the sound
speed of either pure component. In numerous geologic situations the
sound speed of such two-phase systems may be of interest: in the
search for magma reservoirs, in seismic exploration of geothermal
areas, in prediction of P wave velocity decreases prior to earthquakes,
and in inversion of crustal and upper mantle seismic records. Probably
most dramatically, fluid flow characteristics during eruptions of
volcanoes and geysers are strongly dependent on the sound speed of
erupting two-phase (or multiphase) fluids. In this paper the sound
speeds of water, air, steam, water-air mixtures, and water-steam
mixtures are calculated. It is demonstrated that sound speeds calculated
from classical acoustic and fluid dynamics analyses agree with results
obtained from finite amplitude �vaporization wave� theory. To the
extent that air and steam are represented as perfect gases with an
adiabatic exponent ?, independent of temperature, their sound speeds
vary in a simple manner directly with the square root of the absolute
temperature. The sound speed of pure liquid water is a complex function
of pressure and temperature and is given here to 8 kbar, 900�C. In
pure water at all pressures the sound speed attains a maximum value
near 100�C and decreases at higher temperatures; at high pressures
the decrease is continuous, but at pressures below 1 kbar the sound
speed reaches a minimum value in the vicinity of 500��600�C, above
which it again increases. The sound speed of a water-air mixture
depends on the pressure, the void or mass fraction of air, the frequency
of the sound wave, and, if surface tension effects are included,
on bubble radius. The admixture of small volume fractions of air
causes a dramatic lowering of the sound speed by nearly 3 orders
of magnitude. The sound speeds of the pure liquid and gas end-members
are nearly independent of pressure, but the sound speed of a mixture
is highly dependent on pressure. Calculated values for water-air
mixtures are in good agreement with measured values. The sound speed
in a single-component two-phase system, such as a water-steam mixture,
depends on whether or not equilibrium between the phases on the saturation
curve is maintained. Heat and mass transfer which occur when equilibrium
is maintained cause the sound speed to be much lower than under non-equilibrium
conditions in which heat and mass transfer are absent. The sound
speed in a water-steam mixture may be as low as 1 m s?1.

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  • Susan Werner Kieffer

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