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Two separated air bubbles (radii 0.004 m...

Two separated air bubbles (radii `0.004 m and 0.002m`) formed of the same liquid (surface tension `0.07 N//m`) come together to form a double bubble. Find the radius and the sence of curvature of the internal film surface common to both the bubbles.

Text Solution

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`P_(1) = P_(0) + (4T)/(r_(1))`
`P_(2) = P_(0) + (4T)/(r_(2))`
`r_(2) lt r_(1)`
So, `P_(2) gt P_(1)`
i.e., Pressure inside the smaller bubble will be more. The excess pressure
`P = P_(2) - P_(1) = 4T ((r_(1)-r_(2))/(r_(1)r_(2)))`
Let R be the radius of interface then,
`P = (4T)/(R)`
So, `(4T)/(R) = 4T((r_(1)-r_(2))/(r_(1)r_(2)))`
`R=(r_(1)r_(2))/(r_(1)-r_(2))`
`R=((0.006)(0.004))/(0.006-0.004)`
`=((0.006)xx(0.004)^(2))/(0.002)=0.012`
R = 0.012 m
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