regen issues - a bucket of balls...

[matt brown]

As a newbie here, I'm still scanning the threads, but thought of some regen issues that might entertain you guys. 20 yrs ago, I was on a couple popular yahoo boards when various regen stuff came up. There were many spins, but the main theme centered on porosity, and quickly focused on 'steel wool' vs 'ball bearings'. Well, steel wool is a fuzzy option (lol) which depends upon how tightly packed it is, so, we somehow settled on mulling over ball bearings. The starting point was porosity of 'cube stack' vs random stack, and cube stack was a no brainer, since nothing more than ratio of cube to sphere (with a porosity a tad less than .50). However, solving random stack was much more challenging, and I couldn't set up an equation, so took to gen'l math...for a few hrs a night over several nights !!! I finally got the answer to 4 decimals then got a PM from moderator (who's a physicist) with the correct equation and wondering what all the hoopla was about. Yikes, it was a tiny equation that somehow I had missed, hexed by a 6 in my equation that nixed solution. OK, so I got the right answer the wrong way and was trashed by a 'rocket scientist' (no offense Lee if you see this) but I discovered something else along the way, thanks to my gen'l math: a bucket of balls is a bucket of balls...a 1 gal bucket of_only_1" balls weighs the same as a 1 gal bucket of_only_ 1/2" balls, or a 1 gal bucket of_only_1mm balls !!! IOW, the same volume of the same size & shape balls weighs the same - when allowing for slight fractional randomness size issues between ball & bucket size.

So, porosity of balls in regen is constant regardless of ball size (when uniform size balls and ignoring slight irregularity of ball size to regen size) BUT the surface area varies linear ball diameter, whereby, small balls are better.

[matt brown]

Oops, need to clarify...the surface area varies_inversely_ linear to ball size. So, half size balls have same porosity, but twice the surface area, etc.