The dissolution rate of Al 2 O 3 into the CaO-SiO 2 -Al 2 O 3 slag system was investigated at 1 873 K by employing a novel experimental method which involved continual measurement of the torque variation on a rotating alumina rod dipped into a molten slag. Measured torque variation was successfully related to the dissolution rate of the rod. The dissolution rate of alumina was found affected by a number of factors: the rate increased with increasing temperature, the rotating speed of the rod, the CaO content in the slag, and the Al 2 O 3 content in the slag for a fixed CaO content. It was found that the dissolution rate was highly dependent on the viscosity and the diffusivity of slags. The activation energy obtained from an Arrhenius type analysis was in the range of 84 kJ mol Ϫ1. It was concluded that the dissolution of Al 2 O 3 into the CaO-SiO 2 -Al 2 O 3 slag system was controlled by the mass transfer in the slag phase. An iso-dissolution rate diagram was constructed for the dissolution of Al 2 O 3 into the CaO-SiO 2 -Al 2 O 3 slag system at 1 873 K.

A sensorless algorithm is developed on the basis of a rotor flux observer in the stationary frame. In particular, it involves a parameter adaptive algorithm for an initial rotor flux like the observer, which was recently proposed by Bobtsov et al. (Automatica, vol 61, Nov, 2015). In the proposed method, the flux observer is linked to the parameter estimator via a compensating term which results from parameter error. This method has a robust property against dc bias errors, i.e., it cures the inherent weakness of the pure integrator (flux observer) to dc offsets which frequently occur in current measurements and voltage estimates. The robust performance is demonstrated through simulations and experimental results. Index terms: Sensorless, nonlinear observer, flux estimator, linear regression form, position observer, voltage offset. NOMENCLATURE α − β Stationary axis reference frame quantities. d − q Synchronous axis reference frame quantities. v, i Stator voltage and current. λ Stator flux. x Rotor flux. η Initial rotor flux. q Subtracted value initial rotor flux from rotor flux. R, L Resistance and inductance of stator winding. ψ m PM flux linkage constant.

The wetting behavior of solid Al 2 O 3 with molten CaO-Al 2 O 3 -SiO 2 was investigated at 1 873 K using the sessile drop method. A new model was developed to represent the time dependence of the contact angle, i.e., the spreading behavior of a liquid drop on a solid substrate. The model takes into consideration chemical interactions which continually take place at the interface between the solid Al 2 O 3 and molten CaOAl 2 O 3 -SiO 2 . By applying the model to the experimental results of the present study the equilibrium contact angle between the liquid slag and solid alumina was determined for a number of different slag compositions, and an iso-contact angle diagram was constructed. The equilibrium contact angle was greatly affected by the slag composition, and it was found that the interfacial tension was the major factor governing the equilibrium contact angle. In the region of low SiO 2 content, the slag with higher CaO content exhibits a smaller contact angle, i.e., better wettability with alumina. For slag with a given CaO/SiO 2 ratio, an increase in Al 2 O 3 results in a corresponding increase in the contact angle, i.e., decrease in wettability. For a given CaO/Al 2 O 3 ratio, the variation of the contact angle with SiO 2 content shows a minimum. The contact angle decreases by increasing the surface roughness of the alumina substrate.