Part VII – July 1968 – Communications - The Relevance of Stokes' Law to the Physical Conditions of Steelmaking

By contrast with viscometry and sedimentation, no actual measurements of the applicability of Stokes' law to steelmaking have ever been reported; instead, the proof for and against Stokes' law has been inferred from the frequently observed phenomenon that inclusions collect in the top scum and the bottom of ingots. As such proof is unsatisfactory, continued reference to Stokes' law in steelmaking, even as a model for calculating the terminal velocities of rising inclusions, should be avoided. In fact, all conclusions that have been reached regarding size, density, and viscosity on the flotation of inclusions could be made more rationally without Stokes' law. A worthwhile exception is that of Mitsche1 who in 1934 used Stokes' law to show not only the expected effects of size, density, and viscosity on flotation but also the beneficial effects of i) melting under a slag layer (now Electro Slag Refining); ii) treating melts with synthetic slags (Ref. 2 gives recent applications); iii) bubbling an inert gas through the melt (recent applications in Refs. 3 and 4); and iv) altering the solid/ liquid interface characteristics. At this point, it should again be emphasized that the boundary conditions for which Stokes' law was derived place enormous restrictions on the law but its application, as noted earlier, can yield useful results in some fields under certain conditions and within well-defined limits. When compared with inclusions, which may be solid or liquid, spherical or irregular, dispersed or coagulated, interacting between themselves and the melt, floating in a liquid which is in a state of motion of varying intensity5 and contained in vessels of various shapes and sizes that may change with time as in a solidifying ingot, the conclusion is obvious-Stokes'