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re: a bubble wall?
29 apr 1996
still thinking about my 12 year old friend who added 1/4 tsp of lemon juice
to her standard bubble mix (1/2 cup green dawn, 3 tbs glycerin, 2 quarts h2o)
to make the bubbles last 111 seconds at 80 f and 506 sec at 45 f, vs 309 sec 
and 185 sec; 1/4 tsp of maple syrup instead made this 431 and 345 sec. what
is a good bubble solution for blocking longwave ir radiation from a house
window? what is that ir wavelength?

black bodies radiate heat at many wavelengths. planck's law describes
a curve with a peak for this, ie at wavelength lambda, a blackbody with
temperature t (kelvin) radiates with an intensity

     e(lambda) = c1/(lambda^5[exp(c2/(lambda t))-1]), where

            c1 = 3.74 x 10^-16 m^2w and 
            c2 = 0.0144 mk.

wein's displacement law says where the peak is: the wavelength corresponding
to the maximum intensity of blackbody radiation is lmax = 2898/t microns.
80 f is about 27 c or 300 k, so the wavelength with max intensity at 80 f is
about 10 microns or 0.0004 inches, ie just less than half a thousandth of an
inch. how can we measure a bubble thickness like that? what makes bubble
walls thick?

compared to the intensity at this wavelength, this blackbody radiates
at some other wavelength l with a relative intensity of approximately

          irel = (lmax/l)^5 x exp(c2/(lmax t)-1)/exp(c2/(l t)-1).

l: 1 micron       10^5        120.5             / 7 x 10^20 = 1.7 x 10^-14
   5 microns      32          120.5             / 14765     = 0.26
   10 microns     1           120.5             / 120.5     = 1
   20 microns     0.031       120.5             / 10        = 0.38
   50 microns     0.00032     120.5             / 1.61      = 0.024

it looks like thicker bubble walls are better, up to the point where the
bubble wall itself begins to be a sideways path between the two glazings.
if the bubble wall were 10 times thicker than the longest interesting
wavelength, (as people think about transmission lines), it might be 500
microns or 0.020" thick, which seems very thick for a bubble. a wall 4" thick
filled with 0.2" bubbles like that would have a 10% water cross section, so
we might think of such a 10' x 10' wall as having a 1' x 1' thermal shunt 
made of water with a thermal conductance of 1 btu/hr. if that were the only
thermal path, that wall would have an r-value of 100... perhaps a bubble
with a given wall thickness is a better insulator at higher temperatures
with shorter wavelengths.

water has an index of refraction of about 4/3, so each air-water interface 
with a sufficiently thick layer of water compared to a wavelength would have
a fresnel loss of about ((4/3-1)/(4/3+1))^2 = 1/7^2 = 2%. a 4" thick wall
with 20 clear 0.2" bubbles in series might have an attenuation of 1.02^20
= 1.5 for ir radiation. not much... we may need smaller bubbles than that,
perhaps with thinner walls and some dye. let's see, an 80 f room loses about
(80-30)/r2 = 25 btu/hr/ft^2 of heat on a 30 f day through an ordinary double
glazed window. two layers of poly film with little greenhouse effect (ir
blocking) have an r-value of about 1.2... and a 1 ft^2 80 f blackbody with
no glazing radiates 0.174e-8(460+80)^4 = 148 btu/hr, while the 30 f world
radiates 100 btu/hr back at it, so it loses 48 btu/hr by radiation, ie the
r-value owing to radiation is about 1 (50/48.) 

an attenuation of 10, ie 1.02^n=10 makes n=ln(10)/ln(1.02)=114 0.035" diam.
bubbles across a 4" wall, at 28 bubbles per inch... how big are the bubbles
that come out of an airstone in an aquarium? what happens if we remove the
fish and fill the aquarium with some interesting soaps and ir dyes (?) and
warm water, and glue some foamboard on the sides (or start with a styrofoam
cooler) and put a glass lid on the top and measure how fast the water cools
with two thermometers and a clock... suppose our cooler is 1' tall x 1' wide
x 2' long with a 1' x 2' glass lid, and the sides are 1" thick r4 white
beadboard, coffeecup foam, with a thermal conductance of coth = 8 ft^2/r4
= 2 btu/hr-f. this situation might be like a bubblewall ceiling under a
clear polycarbonate roof, with natural daylighting and vertical heatflow. 

without the bubbles, we might have a thermal conductance of coth + 2 ft^2/r1
= 4 btu/hr-degree f. with bubbles, the conductance might decrease to
coth + 2/rx, close to 2 if rx is large. so if we filled the cooler it with 
8" of 130 f water, ie 80 pounds of hot water, we might expect the box with
no bubbles to lose (130-70)4 = 240 btu to a 70 f room in an hour, reducing
the water temp to 130-240/80 = 127 f. the box might be 124 f after 2 hours
or 70+(130-70)exp(-4/20) = 119 f after 4 hours, since the rc time constant
of the box would be about 1/4*80 = 20 hours with no bubbles. (after the
first hour, the water is cooler, so it loses less heat in the next hour,
so the temperature drops less in the next hour, etc.)

if we measure a water temperature of tb (f) after 20 hours, with bubbles,
and tnb without bubbles, what is rx? t = 70+(130-70)exp(-20/rc), so
rc = -20/ln((t-70)/60) = r x 80, so r = -1/(4 ln((t-70)/60). suppose we
measured tnb = 92 f and tb = 106 f. then rnb = -1/(4 ln((920-70)/60) =
0.24918 f-hr/btu and rb = 0.48940, so 1/rnb-1/rb = (coth+2/r1)-(coth+2/rx)
= 2 - 2/rx, so rx = 2/(2+1/rb-1/rnb) = 2/(2+2.0433-4.0132) = r33.

dr. aristid grosse made bubbles that lasted more than a year, as did belgian
physicist joseph plateau in the 1800s. dr. grosse's principles of bubble
health and long life are: 1. dust is the enemy of bubbles. 2. carbon dioxide
poisons bubbles (better bubbles are blown by non-humans), and 3. bubbles
love cold. they also like humidity. glycerin helps bubbles fight humidity.
maybe we don't need it inside a glazing cavity with 100% humidity.  

perhaps this should be a closed system, to avoid building up dust.
something like this? 

		       |  ----------------------    |
       sand filter?--> | |             <--     |    | <--bubbles
                       | |                     |    |
                       | |   ----------        |    |
                       | |  |  -  air  | -->   |    |
                       |  --  | | pump  ----   |    |
		       |  ----  ----------  |  |    | <--water
                       |w|                | |  |wwww| <--water level
		       | |                |  --     |
		       | |                 ----     |
		       | | water return->      |    |
                       |  ---------------------     |

let's all try to invent an insulating bubble wall, perhaps starting with
two pieces of glass or single-layer polycarbonate plastic with butyl tape or
caulk over a plastic 1x3" or foamboard frame that can be filled between with
bubbles at night emerging from an aquarium airstone immersed in a soapy
solution at the bottom. this could really be useful in a passive solar
house or a greenhouse, like beadwall. simple, elegant, movable insulation.
during the day, the sun shines in on some thermal mass, and at night the
glazing fills up with bubbles, keeping the heat in. commercial greenhouses
use two huge layers of uv-treated polyethylene film inflated to form an
air pillow 4" thick. a tiny 50 watt blower can inflate a 1 acre greenhouse.
would bubblewalls work with poly film pillows?

bubbles tend to last longer in cold humid conditions. a layer of frozen
bubbles inside an outside glazing might be very good insulation on a very
cold night. perhaps there is an optimal bubble size for insulation. too
small, and convection losses might be small, but conduction losses and air
pump power and water transport thermal losses might be large. too big, and
convection losses go up. 

ohm's law for heatflow is a good starting point here: the amount of heat q
in btu/hour that flows through a wall with area a ft^2 and r-value r and
temps ti (f) on one side and to on the other, is q = (ti-to)a/r. 

here's another bubble wall test setup, a 2' cube divided in half by a bubble
wall that might have an r-value of 2 when empty and 20 when full. we might make
the cube out of 2" styrofoam with an r-value of 10. one side could be kept
at 32 f with some melting ice at the top, with some foam on top and around
the window screen ice tray, and the other side could be kept at 132 f with
a thermostat and a light bulb, with a piece of aluminum foil to shade the
bubblewall from the bulb. how much ice water might we collect in an hour with
the bubblewall empty and full of bubbles? this might be a more accurate way
to measure the r-value than the aquarium way, especially since house windows
are usually vertical, with lower heat losses. what might we get for readings
in each case if we hook up the light bulb to a kwh meter? it's nice to have
two ways to check the heatflow through the bubble wall.

                       .........................      70 f room
                    .   ice     ..          .  .
                 .........................     .
                 .           ..          .     .
                 .    to     ..  ti      . r10 .  2'
              2' .    32 f   ..  132 f   .     .
                 .           ..  light   .     .
                 .           ..  bulb    .  .
                 .........................    2'
                       1'         1' 
                             |___ bubble wall

it takes 144 btu to melt a pound of ice, and there are 3410 btu in a kwh.

here is the following electrical circuit analog:

                    iir    32 f       132 f   ier
                      -->   |   <--    |    -->
             70 f ---wwww---*---wwww---*---wwww--- 70 f
                    r10/12  |   rx/4   |  r10/12
                    = 0.83  |          |  = 0.83
                            |          |
                           ---     ^  ---
                        ui ---     |  ---
                            |      ue  |
                           ---        ---
                            -          -

where ui and ue are flows of ice and electrical energy (ui flows down,
in this picture.) 

what would ui and ue be if rx were 2 without bubbles and 20 with bubbles?

in either case, iir = (70-32)x12 ft^2/r10 ft^2 = 45.6 btu/hr flows into
the ice from the room, and ier = (132-70)x12 ft^2/r10 = 74.4 btu/hr flows
out of the light bulb into the room. if rx = 2, an additional
(132-32)x 4 ft^2/r2 = 200 btu/hr flows out of the light bulb into the ice,
and if rx = 20, only 20 btu/hr more flows that way. the total ice and
electrical energy flows would be  

     rx = 2 (no bubbles)                  rx = 20 (bubbles)

ui   245.6 btu/hr (27.3 oz ice water/hr)  65.6 (7.3 oz ice water/hr)

ue   274.4 btu/hr (80.5 watts)            94.4 btu/hr (27.7 watts)


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