Tuesday, August 11, 2015

Anecdote 4: Sometimes advisers are right.

When I was a first-year grad student, I started working in my adviser's lab, learning how to do experiments at extremely low temperatures.   This involved working quite a bit with liquid helium, which boils at atmospheric pressure at only 4.2 degrees above absolute zero, and is stored in big, vacuum-jacketed thermos bottles called dewars (named after James Dewar).   We had to transfer liquid helium from storage dewars into our experimental systems, and very often we were interested in knowing how much helium was left in the bottom of a storage dewar.

The easiest way to do this was to use a "thumper" - a skinny (maybe 1/8" diameter) thin-walled stainless steel tube,  a few feet long, open at the bottom, and silver-soldered to a larger (say 1" diameter) brass cylinder at the top, with the cylinder closed off by a stretched piece of latex glove.   When the bottom of the tube was inserted into the dewar (like a dipstick) and lowered into the cold gas, the rubber membrane at the top of the thumper would spontaneously start to pulse (hence the name).   The frequency of the thumping would go from a couple of beats per second when the bottom was immersed in liquid helium to more of a buzz when the bottom was raised into vapor.  You can measure the depth of the liquid left in the dewar this way, and look up the relevant volume of liquid on a sticker chart on the side of the dewar.

The "thumping" pulses are called Taconis oscillations.  They are an example of "thermoacoustic" oscillations.  The physics involved is actually pretty neat, and I'll explain it at the end of this post, but that's not really the point of this story.  I found this thumping business to be really weird, and I wanted to know how it worked, so I walked across the hall from the lab and knocked on my adviser's door, hoping to ask him for a reference.  He was clearly busy (being department chair at the time didn't help), and when I asked him "How do Taconis oscillations happen?" he said, after a brief pause, "Well, they're driven by the temperature difference between the hot and cold ends of the tube, and they're a complicated nonlinear phenomenon." in a tone that I thought was dismissive.  Doug O. loves explaining things, so I figured either he was trying to get rid of me, or (much less likely) he didn't really know.

I decided I really wanted to know.  I went to the physics library upstairs in Varian Hall and started looking through books and chasing journal articles.  Remember, this was back in the wee early dawn of the web, so there was no such thing as google or wikipedia.  Anyway, I somehow found this paper and its sequels.  In there are a collection of coupled partial differential equations looking at the pressure and density of the fluid, the flow of heat along the tube, the temperature everywhere, etc., and guess what:  They are complicated, nonlinear, and have oscillating solutions.  Damn.  Doug O. wasn't blowing me off - he was completely right (and knew that a more involved explanation would have been a huge mess).  I quickly got used to this situation.

Epilogue:  So, what is going on in Taconis oscillations, really?  Well, suppose you assume that there is gas rushing into the open end of the tube and moving upward toward the closed end.  That gas is getting compressed, so it would tend to get warmer.  Moreover, if the temperature gradient along the tube is steep enough, the upper walls of the tube can be warmer than the incoming gas, which then warms further by taking heat from the tube walls.  Now that the pressure of the gas has built up near the closed end, there is a pressure gradient that pushes the gas back down the tube.  The now warmed gas cools as it expands, but again if the tube walls have a steep temperature gradient, the gas can dump heat into the tube walls nearer the bottom.  This is discussed in more detail here.  Turns out that you have basically an engine, driven by the flow of heat from the top to the bottom, that cyclically drives gas pulses.  The pulse amplitude ratchets up until the dissipation in the whole system equals the work done per cycle on the gas.  More interesting than that:  Like some engines, you can run this one backwards.  If you drive pressure pulses properly, you can use the gas to pump heat from the cold side to the hot side - this is the basis for the thermoacoustic refrigerator.

1 comment:

Anonymous said...

Fantastic! I've used dipsticks like this before and always been curious about how they work. Now my life is enriched for knowing =)