# calculate the value of g required for spontaneous emulsification

**Question description**

The free energy of emulsion formation is given by

DG_{form}
= gDA - TDS_{config}

Where g is the interfacial energy, DA is the increase in surface area from
forming the emulsion and DS_{config }is the configurational entropy which is positive.

The configuration entropy is related to the number of droplets formed and the volume fraction of liquid 2 (the internal phase) by the following expression.(10)

DS_{config} = -nk[lnj +((1-j)/j )ln(1-j)]

j = the phase volume of the emulsion

n = the number of droplets

k = Boltzmman’s constant

If g is low enough emulsification could theoretically occur spontaneously.

Use the formula to
calculate the value of g required for spontaneous emulsification at 25 C for an emulsion of 800
grams of oil with a density (specific gravity) of 0.8 into 1000 grams of water
producing a drop __diameter__ of 0.1 micron.

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