I think I see what you’re asking. If you rinse three times using a third of the water, vs rinsing once using the full amount of water, why would the former be more effective? After all, you’re diluting with the same amount of water.
While there are various complications caused by the contaminant sticking to the side, let’s ignore those and work this out mathematically.
You have a 300ml bottle, and it has 1ml of soap in it. You rinse it once to the top with 299ml of water, and pour it out. Therefore, any soap left is diluted by 300 times, its 1 part soap to 299 parts water.
You have the same 300ml bottle with 1ml of soap in it. You rinse it once to a third full with 99ml of water, and pour it out. At this point, any soap left is diluted by 100 times, so its 1 part soap to 99 parts water. You then repeat this, adding another 99ml of water to the 1ml of residue (which is itself, as we said, 99% water and 1% soap). At this point, its 99 parts water to 1 part residue, and the residue is 99 parts water to 1 part soap, so its 9999 parts water to 1 part soap. We do it a third time, 99 parts water to 1 part new residue (which is 9999 parts water to 1 part soap), and now we’re at 999,999 parts water to 1 part soap; the soap is 1 part in a million.
We’ve used the same amount of water, but by using it over 3 rinses instead of 1, we’ve gone from it being 1 in 300 soap to 1 in a million soap. For most purposes, this is enough to make it essentially clean.
More water just adds to the dilution, but each rinse is multiplied by the effect of the previous rinses. Multiplication makes the numbers go higher, quicker, than addition.
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