# Nucleate Site Density

Liquid microlayer under a vapor bubble at a nucleation site.

The knowledge of distribution of nucleation sites is an important factor in determining the boiling characteristics of a surface under specific operating conditions. The number density of sites, or total number of active sites per unit area, is a function of contact angle, cavity half angle, and heat flux (or superheat) (see figure on the right) i.e.,

${N''_a} = f(\theta ,\phi ,\Delta T,{\rm{fluid properties}}) \qquad \qquad(1)$

For a given local heat flux or superheat, a cavity will be active if Rmin is greater than Rb (see Nucleation and Inception):

${R_{\min }} \ge {R_b} = \frac{{2\sigma {T_{sat}}}}{{{h_{\ell v}}{\rho _v}\Delta T}} \qquad \qquad(2)$

Obviously each cavity on a real surface has a specific Rmin that is a function of geometry and the contact angle. Considering eqs. (1) and (2), one expects that as the wall superheat increases, Rmin decreases and the number of active sites having cavity radii greater than Rmin increases.

Kocamustafaogullari and Ishii (1983) have correlated various existing experimental data of N''a for water on a variety of surfaces and pressure ranges from 1 to 198 atm by

${N''_a} = D_d^2{\left[ {{{\left( {\frac{{{D_c}}}{{{D_d}}}} \right)}^{ - 0.44}}F} \right]^{1/4.4}} \qquad \qquad(3)$

where

$F = 2.157 \times {10^{ - 7}}{\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)^{ - 3.2}}{\left[ {1 + 0.0049\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)} \right]^{4.13}} \qquad \qquad(4)$

${D_c} = 4\sigma \left[ {1 + ({\rho _\ell }/{\rho _v})} \right]/{p_\ell } \cdot \left\{ {\exp \left[ {{h_{\ell v}}({T_v} - {T_{sat}})/({R_g}{T_v}{T_{sat}})} \right] - 1} \right\} \qquad \qquad(5)$

${D_d} = 0.0208\theta \sqrt {\frac{\sigma }{{g({\rho _\ell } - {\rho _v})}}} \cdot 0.0012{\left( {\frac{{{\rho _\ell } - {\rho _v}}}{{{\rho _v}}}} \right)^{0.9}} \qquad \qquad(6)$

where Rg is the gas constant for the vapor. Wang and Dhir (1993a, 1993b) have studied number density for boiling of water at 1 atm on a mirror-finished copper surface, and they provided a mechanistic approach for relating the cavities that are present on the surface to the cavities that actually nucleate.

## References

Kocamustafaogullari, G., and Ishii, M., 1983, “Interfacial Area and Nucleation Site Density in Boiling Systems,” International Journal of Heat and Mass Transfer, Vol. 26, pp. 1377–1387.

Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

Wang, C.H., and Dhir, V.K., 1993a, “On the Gas Entrapment and Nucleation Density during Pool Boiling of Saturated Water,” ASME Journal of Heat Transfer, Vol. 115, pp. 670-679.

Wang, C.H., and Dhir, V.K., 1993b, “Effect of Surface Wettability on Active Nucleation Site Density During Pool Boiling of Water on a Vertical Surface,” ASME Journal of Heat Transfer, Vol. 115, pp. 659-669.