Two separate air bubbles of radii r₁ and r₂ (r₂ > r₁) formed of the same liquid come together to form a double bubble. The radius of the internal film surface common to both bubbles is 

Let r be the radius of the common surface and $\sigma$ the surface tension of the liquid. When the bubbles come together, the difference of the excess pressures on either side of the common surface must be equal, i.e. 

                 $\frac{4\sigma }{r_1}-\frac{4\sigma }{r_2}=\frac{4\sigma }{r}$

which gives $r=\frac{r_1{r}_2}{r_2-r_1}$