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Why two or more mercury drops form a single drop when brought in contact with each other?

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• A spherical shape has the minimum surface area-to-volume ratio of all geometric forms.
• When two drops of a liquid are brought in contact, the cohesive forces between their molecules coalesces the drops into a single larger drop.
• This is because, the volume of the liquid remaining the Same, the surface area of the resulting single drop is less than the combined surface area of the smaller drops.
• The resulting decrease in surface energy is released into the environment as heat.

Proof : Let n droplets each of radius coalesce to form a single drop of radius R. As the Volume of the liquid remains constant,

volume of the drop = volume of n droplets

$$\frac{4}{3}πR^3$$ = $$n × \frac{4}{3}πr^3$$

∴ R3=nr3

$$∴ R =\sqrt[3]{n}\,r$$ ....(1)

Surface area of n droplets =n × 4πr2

Surface area of the drop = 4πR2 = 4π×n2/3r2 ..... from eq. 1

∴ Surface area of the drop = n2/3 × 4πr2

∴ The change in the surface area

= surface area of drop — surface area of n droplets

= 4πr2 (n2/3 — n)

Since the bracketed term is negative, there is a decrease in surface area and a decrease in surface energy. .

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