Metal-slag transfer of impurities

This condition applies when the equilibrium content of the slag of the impurity being transfeiTed would be high, but the bulk of the slag is large compared to the volume of the descending metal particle. When is not much less than 

The comparison of the magnitude of the two resistances clearly indicates whether tire metal or the slag mass transfer is rate-determining. A value for the ratio of the boundary layer thicknesses can be obtained from the Sherwood number, which is related to the Reynolds number and the Schmidt number, defined by 

Usually D, and hence 7 s A m s m- The transfer in the slag phase is therefore rate-determining in the transfer of a solute from die metal to the slag phase. 

When the two liquid phases are in relative motion, the mass transfer coefficients in eidrer phase must be related to die dynamical properties of the liquids. The boundary layer thicknesses are related to the Reynolds number, and the diffusive Uansfer to the Schmidt number. Another complication is that such a boundaty cannot in many circumstances be regarded as a simple planar interface, but eddies of material are U ansported to the interface from the bulk of each liquid which change the concenuation profile normal to the interface. In the simple isothermal model there is no need to take account of this fact, but in most indusuial chcumstances the two liquids are not in an isothermal system, but in one in which there is a temperature gradient. The simple stationary mass U ansfer model must therefore be replaced by an eddy mass U ansfer which takes account of this surface replenishment. 

When only one phase is forming eddy cunents, as when a gas is blown across the surface of a liquid, material is uansported from the bulk of the metal phase to the interface and dris may reside there for a short period of time before being submerged again in die bulk. During this residence time t, a quantity of matter, will be U ansported across die interface according to the equation 

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