Question

Two air bubbles with radii r1 and r2 (r2 > r1) formed of the same liquid stick to each other to form a common interface. Therefore, the radius of curvature of the common surface is:

a) r1 + r2
b) r1 - r2
c) r1 * r2 / (r1 + r2)
d) r1 * r2 / (r1 - r2)

Answer 1

The radius of curvature of the common surface formed by two sticking air bubbles is the product of their radii divided by the sum of their radii. Therefore the correct answer is a) r1 + r2.

Step-by-step explanation:

The radius of curvature of the common surface when two air bubbles with radii r1 and r2 (where r2 > r1) stick to each other is given by r1 * r2 / (r1 + r2). This is the case as the pressures must balance at the common interface between two joining bubbles, and the Young-Laplace equation relates the pressure difference across the surface of a bubble to its radius.

This results in the merged bubble having what is essentially a 'weighted average' of radii, inversely proportional to the individual bubble pressures and sizes.

When two air bubbles with radii r1 and r2 stick to each other to form a common interface, the radius of curvature of the common surface is given by the equation:

1 / R = 1 / r1 + 1 / r2

This equation states that the inverse of the radius of curvature of the common surface is equal to the sum of the inverses of the radii of the individual bubbles.

Therefore, the correct answer is option a) r1 + r2.