**3.1 Adherence force**

When a particle approaches the solid surface or to another particle, both unwetted by the liquid, the formation of a cavity between them becomes thermodynamically favorable, see **Figure 20**. This phenomenon is because the replacement of a particle-liquid interface by a particle-vapor interface leads to a negative change of the Gibbs free energy according to Young's Equation. Once the cavity is formed, an attractive force of adhesions develops, FA, as expressed in the following Equation [50],

**Figure 19.** *Adhesion of alumina clusters and aggregates contained in the liquid flow on the nozzle surface.*

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

**Figure 20.**

alumina particle to the surface of a nozzle refractory is favored by the low wetta-

*Effects of melt-refractory and melt-inclusion contact angles on particle-refractory surface adhesion.*

When a particle approaches the solid surface or to another particle, both unwetted by the liquid, the formation of a cavity between them becomes thermodynamically favorable, see **Figure 20**. This phenomenon is because the replacement of a particle-liquid interface by a particle-vapor interface leads to a negative change of the Gibbs free energy according to Young's Equation. Once the cavity is formed, an attractive force of adhe-

bility of the inclusion and the refractory by the melt.

*Casting Processes and Modelling of Metallic Materials*

sions develops, FA, as expressed in the following Equation [50],

*Adhesion of alumina clusters and aggregates contained in the liquid flow on the nozzle surface.*

**3.1 Adherence force**

**Figure 18.**

**Figure 19.**

**102**

*Schematization of a cavity between a sphere and a plate in a non-wetting system.*

$$F\_A = 2\pi\sigma\_{LV}l + \pi l^2 \Delta P \tag{27}$$

The cavity might be filled with: (1) gaseous components initially dissolved in the melt (2) gaseous components coming from the refractory (3) melt vapor, or (4) liquid phases forming due to a local rise in the oxygen concentration. In any case, there will be a pressure drop between the liquid outside of the cavity and the phase inside of it. The pressure difference obeys Laplace's Eq. (45),

$$
\Delta P = \sigma\_{LV} \left( \frac{1}{r} - \frac{1}{l} \right) \tag{28}
$$

Where l and r are the principal radii of the cavity. The two parameters determine the profile of the liquid–vapor interface, which can be either optimized using the Laplace-Young Equation at constant pressure drop or approximately described with a piece of a circle with radius r. When the cavity is in equilibrium with the liquid phase, its shape is determined by thermodynamics. The estimated adhesion force between an alumina particle and the wall of an AG (alumina-graphite nozzle) is about 25X10�<sup>6</sup> N [51], large enough to keep fixed the particle on the refractory surface.
