Let's do the same thing as we did with cylinders, make our pot scrubber from the material of one marble.
Pot scrubbers are made from long filaments with a rectangular cross section. Typically, the width of a filament is 0.1cm and the thickness 0.001cm, though this varies with different brands. We've done our calculations using these sizes because that's the type we use. You can do your own measurements and calculations with your scrubbers, but the conclusions will be much the same.
Let the width of the cross section of a filament be W and the height H. Let the length be L, and to simplify the math, imagine we can make one long filament out of our marble.
The volume of the filament will be W * H * L, and it will be the same as the marble it came from. Since the 1cm marble has a volume of K / 6,
Amazing, isn't it? Over 52 meters (57 yards) from one small marble!
The surface area is S = 2 * 0.1 * 5236 = 1047.2cm2 (1.1 square feet) (multiply by 2 because it has two sides).
RCP does not apply to a filament, because it is not a solid object like a marble, so we have to make some real-world measurements. We took a quantity of steel scrubber material we'd used in a column (and which had been stretched out so it didn't resist the flow of vapor and liquid), and measured it. Its volume was 464 ml (20 cu. In.) and it weighed 71 grams (2.5 ounces.
The density of steel is 8 gm/ml, so a 1cm steel marble weighs 8ft / 6 = 4.19 gram. The 71 grams of scrubber material is equivalent to 17 marbles. The surface area of a scrubber filament made from one marble is 1047.2cm2, so the total surface of the scrubber is 17 * 1047.2cm2, in a volume of 464ml. Z = 17 * 1047.2cm2 / 464 = 38.4
If you can't find steel pot scrubbers, metal turnings from a lathe work very well. It is impossible for us know the actual value of Z for lathe turnings, because they vary, but it is probably a bit less than 38.4. Since lathe turnings are generally bulkier, you couldn't get as much in a given length of column, but the comparison figures below show that there is plenty of leeway before efficiency drops.
Metal pot scrubbers are available in steel, brass and copper. We've talked about steel ones, because these are the most common. However, some people believe that copper is superior, for the same reasons it is used in whiskey stills. This is a fertile area for experimentation!
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