Experiments were carried out to measure mixing time and slag eye area in two different water model ladles with gas injection nozzle located at the mid bath radius position. Within the range of experimental conditions studied, the following correlations (in SI unit), for 95% mixing time and slag eye area, were found to work satisfactorily:
In the above equations, Q is the gas flow rate (corrected to mean height and temperature of the liquid)(m^{3}/s), L is the liquid depth (m), R is the vessel radius (m), ΔL is the slag layer thickness (m), υ_{s} is the kinematic viscosity (m^{2}/s) of the upper phase, ρ_{L} is the bulk liquid density (kg/m^{3}), τ_{mix,95%} is the mixing time (s), A_{es} is the slag eye area (m^{2}), U_{P} is the average plume rise velocity (m/s), g is the gravitational acceleration (m/s^{2}) and Δρ is the metal-slag density differential (kg/m^{3}). Based on the above and a set of four different bounds on (i) specific energy input rate, (ii) ladle aspect ratio, (iii) amount of liquid in ladle and (iv) slag layer thickness, a multi-objective, constrained optimization problem was formulated to investigate inert gas injection in steelmaking ladles. To this end, a Genetic Algorithm based optimisation procedure embodied in MATLAB™ was applied. Due to the conflicting nature of the objective functions, a Pareto optimal front, comprising many optimal solutions resulted from which the desirable range of operating parameters was identified. Present study has also indicated that desirable optimal operating conditions are likely to be a function of the location of the porous plug in a ladle. Finally, for the sake of validation, three arbitrarily chosen experimental conditions were evaluated against the relevant Pareto front and it is shown that the chosen conditions are, by and large, sub-optimal.