Estimation of Critical Carbon Particle Engulfment Velocity in Metallurgical Melts

Abstract

The critical velocity of engulfing carbon particles in metallurgical melts controls the interfacial area available for the carbon/melts reaction and subsequently dictates the overall pyrometallurgical process. Because of difficulty with high temperature experiments, the relationship of the engulfment velocity and forces acting on the carbon particles has not been well established. In this study, a model based on the principle of force balance and equation of motion has been proposed to estimate the critical carbon particle engulfment velocity for high temperature metallurgical systems. The present model improves upon the existing expressions by including a precise treatment of buoyancy force on particles. The computed results were validated against the experimental data on injection of spheres (glass, stainless steel, sapphire and Hastelloy B) into a mercury bath and were found to be in excellent agreement. The critical engulfment velocities for coal/slag systems were estimated by taking into account the measured carbon/ slag interfacial contact angle. The results were found to lie in between the proposed penetration velocity obtained by using Siderenko correlation and that obtained by using Voronova correlation Using this model for carbon/slag systems (CaO-SiO 2 -Al 2 O 3 -MgO-Fe 2 O 3 ), the critical carbon particle engulfment velocities were found to range from 4.3 to 5.6 m/s for particles 100 μm in size. In carbon/Fe-C-S systems, for particles about 100 μm in size, this value ranged from 2.4 m/s to 7.2 m/s. The critical particle engulfment velocity was estimated as a function of particle size and interfacial contact angle characterising the wettability at the carbon/melt interface. An increase in carbon content of the melt lead to increased values of contact angles and of critical engulfment velocities. Due to poor wettability, engulfment of carbon particles of the same size will be more difficult in melts containing higher carbon levels. It is concluded that for the carbon particles typically employed in metallurgical processes, the wettability between particles and melts has a significant influence on the critical engulfment velocity and therefore could dictate the carbon/melt interfacial area and any subsequent reactions occurring at the interface.