Two soap bubbles with radii of curvature `R_(1) and R_(2)` where `R_(2)lt R_(1)` are brought into contact as shown in Fig. 21.10. What is the radius of curvature of the film between them? What is the contact angle of the films?

Explanation

The pressures from the left and from the right are equal, i.e.
`Delta p_(1)+Deltap=Deltap_(2)= or (4 sigma)/(R_(1))+(4 sigma)/(R)=(4 sigma)/(R_(2))`
Here `Delta=4sigma//R`, for the film has two surfaces--the external and the internal. Hence
`(1)/(R)=(1)/(R_(1))-(1)/(R_(2))`
Since at the point of contact of the three films we have a system of three forces of equal magnitude in equilibrium in a plane, the angle

between the forces is found from the condition that they form a closed triangle.