Applying Young’s equation in the energy change relation (equation 5.16), we have

(5.17)

Below critical radius the nuclei will shrink whereas above , it will be stable and will increase to minimize free energy barrier, . For critical radius, . Applying the above result to equation (100) we get,

(5.18a)

The equation resembles the Kelvin equation. This resemblance in homogeneous and heterogeneous nucleation case is due to a common assumption of nucleus being a part of a sphere.

So the critical potential barrier for heterogeneous nucleation is given by

(5.18b)

Where,

Note: The term in the square braces is same as that in the homogeneous nucleation case. So we can write that the free energy barrier for heterogeneous nucleation is equal to that of homogeneous nucleation multiplied by

(5.18c)