No one else answered Mike, so I will.
It seems that not many actually do this test.

> What kind of container do you recommend to place over the brood area to contain the liquid nitrogen? 

3-inch diameter metal galvanized dryer vent is what everyone uses, 4 to 5 inches long. Don't skimp on depth, as the LN2 will "boil" when you pour it into the cylinder, and you don't want it to boil out of the cylinder. If you want to do this often, try and find the true old-skool galvanized mottled gray stuff, not the el-cheapo shiny silver aluminum stuff. The galvanized type is more sturdy.

> Do you leave the container in place until all the liquid nitrogen evaporates? 

Yes, but this part of the process is not that simple, see below

> How much liquid nitrogen do you place in the covering container?

250 to 350 ml for the 3-inch dryer vent sized cylinder.  But this is also not that simple, see below.

FREEZIN' BEEZ
=========

Jerry Bromenshank is the one who came up with this approach, as Jerry likes playing with things like -320F liquids and re-purposed Latvian military surplus hardware.  If he contradicts me, then I guess I've been doing it wrong all these years.

I've never done more than one frozen patch per hive, but several people have done several patches per hive.
I'm not clear what the rationale is for that.  My only concern is to merely test what I have been sold as "hygienic".
I use the standard-issue naval aviator excuse - "I don't build 'em, I don't fix 'em, I just fly 'em".

First off, you need VERY heavy gloves, work boots, and a metal-shop plastic face shield (not just safety glasses!).  I'd wear something thicker than a tee-shirt, and long-sleeved too. When you pour, the stuff can splash, and it only takes a tiny droplet on skin to ruin your afternoon.  I have rock-steady hands, and I splash this stuff.  You also need big Styrofoam coffee cups, 12oz or 16oz.  You can't use anything but Styrofoam, as the LN2 will freeze and crack non-Styrofoam cups. 

When you pour, you must wear gloves, and you pour from the official (dewar) flask into the cup, with the cup sitting on a level firm surface.  You then put down the flask, and pick up the cup, and pour from the cup into the comb cylinder.  This limits the potential spill factor, and gives you better control, as you can see the level in the cup, and muse about it being half full or half empty. 

NEVER hold the cup in your hand when pouring into it.  Not even once. You need those fingers to keep bees.

Find a comb with a area of "solid" sealed brood.  A 3-inch diameter circle covers about 150-160 cells. Shake/brush off all bees.
Lay the comb down flat. Take the metal cylinder, and "twist it in" like a biscuit-cutter to cut halfway into the comb.  I use wired wax for all my brood combs, so the wires encourage a good stopping point.  

Photograph the cells inside the cylinder, and the cylinder position on the frame, so you can later count the number of non-sealed cells.  This matters for the math.  The overall photo of the frame is to remind you of where the frozen area is, so you can document the work of that rare hygienic colony that cleans things up so fast that you wonder if you had skipped it and not done the test at all.  (I used to count cells and take notes, but digital cameras now come as free prizes in cereal boxes, so now I say "photograph".)  It also helps to mark the frame tested with a Sharpie or a thumbtack, so you don't forget which frame was tested.

Pour about 1/4 coffee cup of LN2, just enough to cover the cells, and wait until you see the vaporization around the edges that shows freezing of at least the cappings has happened. This should take about a minute.  Now pour the rest of the LN2 (methodologies say anywhere from 200ml to 350ml in total is used per hive) into the cylinder, and let it sit until all the LN2 has evaporated away, and the can is no longer "frosty".  I'd give it a good 8 to 10 mins.  Then pull the cylinder off and put the frame back in the colony.  If you buy multiple cylinders, you can start the next before the first is done.

I have seen some methodologies say that the "frozen" frame was invariably placed "in the center" of the broodnest, but I think it much better to replace it exactly where one found it.  If one is going to take so much care and trouble to kill brood without disturbing the comb, then it would be a far bigger disturbance (from the point of view of a bee) to misplace the frame within the broodnest.  Not disrupting the shape of the brood sphere, means that all the tomato (or watermelon) slices on the frames have a specific place within the current brood sphere. The brood sphere is likely more oblate than spheroid, so we should be calling it a brood "watermelon".  (I'd say "football", but most of the world plays "football" with a spherical ball.)

48 hours later, you come back and record the results, so snap another photo of the same area of the frame, and remove the thumbtack if you used one.  Count the number of cells still sealed within the frozen area.  The interpretation of results should include more than a simple count of "opened" vs "sealed" cells.  The actual results prompt a gestalt evaluation, with results ranging from tepid ("only uncapped a few cells, did not clean them") to "Holy Grail" ("so cleaned and repaired, there is no perceptible trace of comb section having ever been frozen").   There is clearly a need to account for colony strength in the testing, so this also factors in.

Did I mention that transporting LN2 in a pickup truck or Volvo is fraught with potential for hazard, and that it should be ratchet-strapped down?

Did I mention that a working and un-clogged relief valve is required to prevent your LN2 flask from becoming a explosively-propelled sub-orbital projectile?


Also, consider for a moment the humble, safer, and far cheaper Co2 fire extinguisher:
 
Co2 "boils" at -70F (-57C)  
Dry ice sublimates at -109F (-78C)  
LN2 "boils" at -320F (-195C)

Sure, LN2 is a lot colder, and I've read that dry ice (solid Co2) did not do the trick in some tests. Could that have been a Leidenfrost artifact?  The surface contact between a hunk of dry ice and comb cappings has got to be less-than perfect, and the "pre-pour" approach with the LN2 clearly is intended to overwhelm the Leidenfrost effect before pouring in the main bulk of LN2.

I've never seen the data or heard any explanation as to why we can't expect a good solid brood kill with -70F Co2 applied to the cappings for a reasonable period.   Jerry?  Anyone?  Shoot the fire extinguisher into the cylinder every second for 20 seconds? If I keep hitting the comb with Co2, why don't I get a frozen-solid mass at some point? 

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