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Surface Tension

Two separate ...

Question

Two separate bubbles (radii 0.002 m and 0.004 m) formed of the same soap solution (surface tension = 0.07 N/m) comes together to form a double bubble. The internal film common to both the bubbles has radius $R$ . The value of $R$ (in mm) is (Answer upto two digit after the decimal point)

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Solution

Excess pressure is always present on concave side. So interface is concave towards small bubble.
$p_{1} = p_{o} + \frac{4 T}{r_{1}} p_{2} = p_{o} + \frac{4 T}{r_{2}}$
Excess pressure $= p_{1} - p_{2} = 4 T (\frac{1}{r_{1}} - \frac{1}{r_{2}}]$
This excess pressure for the interface is also equal to $\frac{4 T}{R}$ .
$∵ 4 T (\frac{1}{r_{1}} - \frac{1}{r_{2}}] = \frac{4 T}{R} R = \frac{r_{1} r_{2}}{r_{1} - r_{2}} = \frac{(0.002) (0.004)}{0.004 - 0.002} = 0.004 m = 4 m m$

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