The principles of metal extraction

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

The comparison of the magnitude of the two resistances clearly indicates whether the 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 Ds DM, and hence Rs Km sRm- The transfer in the slag phase is therefore rate-determining in the transfer of a solute from the metal to the slag phase. 

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

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

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