**Greek letters**

and the alumina particle's population responsible of the nozzle clogging. The high level of supersaturation required by aluminum governs the initial size distribution. Once the particle is nucleated at the initial stages, the initial growth is through diffusion and Ostwald ripening mechanisms. Although not proved yet here, the published literature reports that the bond strength among alumina particles and their morphology are important on the clogging mechanism. Once inside the nozzle, the particle, taking contact with refractory, may remain adhered to it if the adhesion force is larger than the momentums originated from the lift, buoyancy and

The refractory's roughness is of no help to control the clogging as those materials that are hydrophobic or hydrophilic will enhance these properties with rough surfaces. Ideally, a smooth surface approaching the Young's Law would be the ideal material to decrease clogging. Raw materials purity is of interest as some oxides are easily reduced by the carbon of the nozzle or aluminum in the melt, all working to

Under the present situation, this work contributes to the understanding of the surface phenomena in the areas of inclusion nucleation and growth of inclusions and the steel refining and the interaction with the refractory. It gives options for the boundary conditions applied in computational fluid dynamics simulations, all

drag forces with the particle size.

*Casting Processes and Modelling of Metallic Materials*

enhance the clogging problem.

**Nomenclature**

focused on designing new nozzle materials.

dp Particle diameter

f Correction factor

*g* Gravity constant hi Henryan activity of i *I* Nucleation rate kB Boltzmann's constant *l* Principal radii No Constant P Pressure r Inclusion radii

r0 Initial radii of the inclusion

R Gas constant and particle radii

rc Critical nuclei radii

R1 Particle 1 radii R2 Particle 2 radii S0 Supersaturation

T Temperature

x Neck radii

**106**

VO Oxide molar volume

Wad Work of adhesion

t Time

F Force

CO Oxygen concentration in the melt CP Oxygen concentration in the oxide

DV Coefficient diffusion of vacancies

DO Diffusion coefficient of oxygen in the melt

Fs, Fv Surface fraction of solid and vapor phase, respectively

w Collision probability of two particles in turbulent flow regime

Ws Probability for collisions for two particles in Stokes's regime

