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Behavior of Al
If one takes the term assumed constant in Eq. 5, k,,‘PsAs — + — , and views it in
context of the experiment performed some assumptions can be made. As should be close to constant if one assumes that the quenching is instantaneous, only allowing reactions at 1600 °C. mm and ms can also be considered constant as the mass of the crucible did not change to any large degree from before and after the experiment. The concentration of the slag should not change drastically under the experiment allowing for ps and Кй to also be roughly considered constant. ki;t is then the only parameter left. Sample set CSA404020 shows a behavior akin to the one expected if ki;t is constant. The other samples setts show large deviations from this behavior, and call for a ki;t that changes drastically with respect to time. For this to fit it must allow multiple changes of magnitude with respect to time, to allow for the peaks seen in the experimental data. Since lim x = ю°°, the behavior of kit must
additionally be of such a form that (J0 ki;tdt) ! 1. This does not seem likely
Table 3 Slag viscosity calculated from the viscosity model proposed of Kondratiev and Jak 
based on the fact that the phase parameters do not change this drastically to commend this. Fluid flow and geometry changes could have contributed, but there is no significant fluid flow, and the geometries should be constant. Slag viscosity is something that has been looked at and the slag viscosity for the sample setts are shown in Table 3, calculated using the viscosity model proposed by Kondratiev and Jak .
Using the same model for small changes in slag concentration shows that the slag viscosity does not change much there either. One thing which is interesting however is that the sample set with the lowest viscosity behaves more akin to the base model, while the sample set with the highest viscosity has the largest initial deviation. This can be seen in Fig. 7, where the concentration of Al has been normalized with respect to the 180 min sample. From Fig. 7 it can be seen that if the 5 min sample for the sample set CSA255520 was removed as being an outlier then the behavior of the sample looks somewhat like the batch model . The problem with this still is that the relative initial mass transfer rate from the experimental data is higher with increasing slag viscosity. If all the plot points are considered then it looks like the points oscillate around the curve expected from this model. This relationship is also shared with the industrial data for Al from Kero et al. . The industrial data in Fig. 2 show that Ca’s behavior closely resembles the batch model, while Al has a behavior more akin to the experimental data found here. Since the traditional batch model does not take into consideration the effect the distribution equation between Ca and Al, reaction 5, this might allow for the behavior seen here. While it is highly speculative it might still be considered.
If one assumes that the metal initially contains no Al and Ca then the initial mass transfer should be high due to the ease at which the impurity atoms can move across the reaction interface. When the impurity atoms then enter the metal they can quickly diffuse into the bulk away from the reaction surface allowing new atoms to take their place. This leads to reaction (5) becoming unbalanced, which in turn should increase the probability of the offending species atoms to move from the metal into the slag. For this to happen the offending species atoms need to be present at the metal interface in a large enough concentration to restore the balance
Fig. 7 Normalized concentration of Al with respect to the 180 min sample for each sample set respectively dictated by reaction (5). As the concentration of impurity atoms increases the impurity atoms movements become more constrained increasing the probability that an impurity atom is present at the metal interface. If this is the case then it is not unreasonable that the impurity concentrations might overshoot their expected value. A higher slag viscosity should lower the rate at which the impurity atoms diffuse in the slag, which in turn should increase the residence time of an impurity atom at the slag interface before it can diffuse into the bulk slag. It follows that reaction (5) should then act slower in slags with a higher viscosity allowing a bigger overshoot of impurities in the metal. When the concentration of impurities in the metal becomes high enough it may in turn be favorable to move into the slag causing a new overshoot in the slag. If this occurs continuously where each iteration causes an overshoot which is lower than the previous it can be expressed as an oscillating behavior. For each oscillation there should be a higher readily amount of particles at the interface decreasing the overshoot amount of the species. This thought is somewhat interesting as when one superimposes a damped harmonic motion on to the batch model it provides a better fit for the experimental values, but there is not enough data to support this theory, and with itself it brings other problems.
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