ï»¿ Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles. Take a < b and surface tension of soap liquid 'a' is T. from Physics Mechanical Properties of Fluids Class 11 Manipur Board

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Two soap bubbles of radii 'a' and 'b' of same liquid come together to form a double bubble. Find the radius of curvature of common interface of two bubbles.
Take a < b and surface tension of soap liquid 'a' is T.

Given, two bubbles of radii 'a' and 'b'.Â

Let,

p1
be the excess of pressure inside the bubble of radius 'a', and

p2 be the excess of pressure inside the bubble of radius 'b'.

Therefore, we have

P1=4TaÂ Â andÂ P2=4Tb

The two bubbles come together to form a big bubble.

Then let r be the radius of common interface.

Now the difference of pressure on the two sides at interface is given by,Â

Â  Â

'r' is the radius of curvature of common interface of two bubbles.Â
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