The detection of solutal convection during electrochemical measurement of the oxygen diffusivity in liquid tin
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INTRODUCTION
M E A S U R E M E N T of the oxygen diffusivity in liquid metals at elevated temperatures by coulometric titration using solid oxygen-ion conducting electrolytes has been performed in many systems since its introduction by Alcock and Belford. t~l A variety of experimental cell designs, diffusion geometries, and titration procedures have b e e n u s e d . [2,3,41 In these measurements, a solid-state electrochemical cell can be used to establish a known concentration boundary condition (potentiostatic experiment), known flux boundary condition (galvanostatic experiment), or to measure the oxygen concentration (galvanic operation). Cylindrical geometries have been most often used, with unidirectional transport in the radial or axial directions. Analysis of both transient and steady-state data has yielded information on the transport of dilute oxygen in liquid metals. As summarized by Odle and Rapp 141 and Ramanarayanan and Worell, ts] several factors limit the successful application of such measurements to high-temperature liquid metal systems. These factors include oxygen short circuiting through local cell action or gas-phase transport, interaction with container materials or gas ambient, electronic conduction in the solid electrolyte, and reference electrode polarization. In particular, convective flows in the melt are a problem, since typical diffusive velocities are of the order of 10 -3 mm/s. To remove convective effects in these molecular diffusivity measurements, thermal gradients which induce natural convection must be eliminated or at least substantially minimized. Previous investigations of oxygen diffusivities in liquid tin, and in other liquid metals, have generally not taken sufficient care to eliminate thermal B. SEARS, formerly Graduate Student, Chemical Engineering Department, University of Florida, is Medical Student, Medical School, Ohio State University, Columbus, OH. T.J. ANDERSON, Professor and Chair, and R. NARAYANAN, Professor, are with the Chemical Engineering Department, University of Florida, Gainesville, FL 32611. A.L. FRIPP, Senior Scientist, is with NASA (Langley) Research Center, Hampton, VA 23655. Manuscript submitted February 17, 1992. METALLURGICAL TRANSACTIONS B
gradients. Indeed, some researchers I61 have even imposed small thermal gradients across their experimental cells (increasing temperature with height) in order to "stabilize" the melt. Such gradients, however, are expected to have adverse effects in the creation of small horizontal thermal gradients due to mismatching of thermal properties of the melt and its container. Hurst tTj modeled this particular case numerically and observed low-level convection of sufficient magnitude to cast doubt on the reported results. In the presence of gravity, a static fluid is unconditionally unstable to any horizontal density gradients, i.e., density gradients that are not parallel to the gravity vector. This can be easily proven through manipulation of the Navier-Stokes equations, tSl A detailed discussion of the effects
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