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Find the lifetime of a soap bubble of radius R connected with the atmosphere through a capillary of length l

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Find the lifetime of a soap bubble of radius R connected with the atmosphere through a capillary of length l and inside radius r. The surface tension is α, the viscosity coefficient of the gas is η.

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Suppose the radius of the bubble is x at some instant. Then the pressure inside is  p0+4α/x. The flow through the capillary is by poiseuille's equation,

 

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