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bubbles

 Definition/Summary The rate of rise of a bubble in a liquid is a function of liquid density, viscosity and surface tension. Each is a function of liquid temperature. Other relevant properties need to identified, e.g., bubble size, and equations developed to predict rate of rise in a particular liquid. They may include the liquid properties or possibly just the temperature.

 Equations The velocity of rise of an air bubble was found to follow: $$U = \frac{2}{3}\sqrt{gR}$$ where R is the radius of the bubble. (From Davies and Taylor; see full reference below.)

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 Breakdown Physics > Classical Mechanics >> Fluid Statics

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 Extended explanation Reference: "The Mechanics of Large Bubbles Rising through Extended Liquids and through Liquids in Tubes", R. M. Davies; Geoffrey Taylor, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 200, No. 1062. (Feb. 7, 1950), pp. 375-390. In this paper two types of fluids were tested, water and nitrobenzene (oil). The agreement between theory and their experimental results was excellent according to the paper.

Commentary

 Redbelly98 @ 07:59 PM Nov27-09 I can only suggest looking up the paper by Davies and Taylor for the reasoning behind the equation. Just as an educated guess as to why density is not important, it's probably similar reasoning to why freefall acceleration is independent of an object's mass or density.

 Bob Higgins @ 10:31 PM Nov26-09 Thanks for the formula but I would like to know why properties of the liquid are not a factor because drag of the near sphere must balance bouyant force.

 Redbelly98 @ 06:11 PM Nov12-09 Thanks to stewartcs for telling me about the paper by Davies and Taylor. Problem: the equation from Davies and Taylor shows no dependence on density, viscosity, or surface tension, as asserted in the Definition/Summary section.

 tiny-tim @ 04:16 AM Nov12-09 I've changed the title from "Bubble Rise in a Liquid" to "bubbles", since the whole point of the PF Library is its autolinking, and this page will never be looked at unless there are threads with the title words to click on. But as "bubbles", it needs to be wider in scope.