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The interface is usually a few molecules thick but its area depends on the size of the particles of the bulk phases.

*What is Area of interface? What is its sense and How is it defined.I mean if we have two bulk faces with significant difference in particle size,and we define surface area for one layer then it is surely not the same as that for the other layer then how that area of interface make sense.

One of the explanation (or i should rather say an example) i found on internet is oil dressing on salads ,where interface is spherical having less surface area.

Now that example is itself confusion because it is mathematically proved that for any given volume sphere has least surface area, then how is that area being less attributed to particle size?

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Area of interface is the area of contact between two phases. If one phase is dispersed in another one, it then consists in the sum of the surface for each particle/droplet.

If you consider a spherical particle, its surface is $S=4\pi r^2$ and its volume $V=\frac{4}{3}\pi r^3$. Now consider the ratio $\frac{S}{V}=\frac{3}{r}$, so when the size of a sphere (but it is true for any shape) diminishes, the ratio $\frac{S}{V}$ increases. In other words, if you take an initial volume that you divide in small spheres, the global volume does not change (the sum of all spheres) but the surface increases.

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