Drops and surface tension

Question

When a drop of liquid splits into a number of drops, each drop tries to minimize its area but the overall surface area of drops increases. How does the overall surface area of the drops increase????

Answer 1

It does not try to minimize it's total surface area,rather it minimizes it's $\frac{surface \\\ area}{volume} $ ratio to attain minimum potential and thus the droplets assume spherical shapes as it is the best way to do so.

Answer 2

How does the overall surface area of the drops increase????

It’s just geometry.

The area of a sphere with radius $r$ is $A=4\pi r^2$ and the volume is $V=\frac43\pi r^3$, so the relationship between area and volume for one sphere is

$$A_1=4\pi\left(\frac{3V_1}{4\pi}\right)^{2/3}=CV_1^{2/3}$$

where $C$ is a numerical constant.

Now suppose one sphere of volume $V_1$ divides into $N$ spheres each of volume $V_1/N$. Their total area will be

$$A_N=NC\left(\frac{V_1}{N}\right)^{2/3}$$

or

$$A_N=N^{1/3}A_1.$$

Thus the area increases as the cube root of the number of spheres.