Bubbles in Beer, Dust in Air, and Why they Matter

I'm giving a talk this weekend at a meeting of the Jefferson Land Trust in Port Townsend. One of the points of the talk is that fluids of interest in geological processes can have some very unusual and unexpected properties. One example relates to the speed of sound in a liquid or gas.  The speed of sound in liquid water is about 1400 meters per second, basically a mile per second. That's fast compared to geological processes which typically have speeds less than a few hundred meters per second. But, if the liquid has gas bubbles, for example boiling water, the sound speed is dramatically depressed. Why? Consider first a simpler fluid than boiling water: beer. The sound speed (squared) is defined as the inverse of the compressibility*density.  Compressibility is "squishiness." Water isn't very squishy (as anyone who has done a belly flop off of a diving board knows), but if you add bubbles, things change (there's a reason that Olympic high-divers plunge into an aerated part of the pool). The density isn't affect much at all by the presence of small bubbles, but the squishiness is dramatically changed--the bubbly beer has almost got the squishiness of the bubbles. So, since the squishiness is in the denominator, the sound speed dramatically decreases--down to about 10 m/s. If the bubbles are steam in water, instead of air, there are other processes (condensation and evaporation of the steam as sound waves pass) the sound speed can be even lower, as low as 1 m/s. That means that if we walk at a pace of ~20 minutes per mile, and could walk through boiling water, we would be walking at Mach 2!!

     There's another situation in which low sound speeds can occur in geologic processes: dusty gases. The sound speed of a pure gas is inversely proportional to its molecular weight. The higher the molecular weight, the lower the sound speed: Helium ~ 970 m/s; Air ~340 m/s; Freon 12 ~150 m/s. I haven't done a lot of research on particle concentrations in dust storms, but in one study in Australia, concentrations of 10 mg/m3 for just the breathable particles were reported. If anyone wants to help convert this to mass fraction (mass ratio solids:vapor), help is welcomed!
     It is very difficult to determine particle loading in volcanic eruptions. Any sensors in the path of advancing gas/particle clouds are destroyed, but remote sensing techniques are improving.  The bottom line is that particle loading in destructive emissions are high compared to even desert dust storms, thus their destructiveness. These flows can be "internally supersonic," that is, supersonic inside themselves, but subsonic compared to atmospheric sound speeds (~340 m/s). Thus, they don't generate shock waves. The lateral blast at Mount St. Helens did not generate atmospheric shock waves. It did generate compression waves as the blast pushed on the atmosphere, and due to the complex structure of the atmosphere, these waves steepened into audible acoustic waves to the north, e.g., hear in Vancouver B.C.
     Bottom line: there are shocks and there are shocks. Some are inside these wierd geological flows, and others are in the domain of atmospheric sciences.