# calculate the value of g required for spontaneous emulsification

Sigchi4life
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Physics
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Question description

The free energy of emulsion formation is given by

DGform = gDA  - TDSconfig

Where g is the interfacial energy, DA is the increase in surface area from forming the emulsion and DSconfig 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)

DSconfig  = -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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