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What family sayings did you think was universal?
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Funny my grandad had a little rhyme related to your ketchup effect:
"If you do not shake the bottle, none'll come and then a lot'll"
Clearly ketchup bottles have been a bigger influence on culture than we realised
Shaking the ketchup bottle is a great pro tip. No idea why it works but it does.
Vigorous shaking mixes the thicker areas (where the sauce has settled) and the thinner (more watery) areas so they now have the same viscosity (pouring characteristics). Most importantly, this lets the mass of sauce slide cleanly down the bottle, helping the air bubble to also slide up in one unit at the same time, preventing the “air-lock” blockage at the opening. Important Note: Before vigorously shaking any container, ensure that the cap is truly secured! Now you are in control!
I think what you said is true but that also ketchup as a material is shear thinning—meaning as you shake or tap the bottle, this creates stress or “shear” on the liquid which causes the viscosity to decrease. It also takes a little bit of time for the liquid to re-thicken, so it will actually pour pretty well a few seconds after shaking it.
https://www.scientificamerican.com/article/ketchup-is-not-just-a-condiment-it-is-also-a-non-newtonian-fluid/
Bravo!