Page 188 - Reservoir Formation Damage

170 Reservoir Formation Damage

(9-11)

The depositing substance and the substrate surface match well when
a <a an
cs cH" d GCS is negligible and G SW=G CW for perfect matching
(Schneider, 1997).
Thus, the critical minimum radius necessary for formation of stable
particles can be determined by equating the derivative of Eq. 9-11 with
respect to the radius to zero as:

(9-12)
AG,+e

Then, substituting Eq. 9-12 into Eq. 9-11 yields the expression for the
activation energy necessary for formation of stable particles as:

(9-13)
3(AG v +ef

For homogeneous nucleation, A cs = 0 and Eq. 9-6 simplifies to

AG = VAG v+A cvva cvv + Ve (9-14)

Approximating the shape of the deposit by a sphere of radius r such that

3
V = -nr (9-15)
3

= 471 r 2 (9-16)
A cw

Eq. 9-14 can be written as

3
2
AG (r) = - 7cr (AG v + e) + 4jcr a c (9-17)