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Demonstrate (i.e., with a proof instead of a specific example) that fusing two identical spherical droplets...

Demonstrate (i.e., with a proof instead of a specific example) that fusing two identical spherical droplets of some dispersed liquid into a single new spherical droplet reduces the collective surface area by 21%. Why is this fact important for emulsion stability?

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Emulsions are made by mixing up of two phases, so decrease in surface area reduces the surface tension in the droplets which helps in easy mixing up of the two phases.

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